Deck 1: Equations, Inequalities, and Applications

Question 1

Use slope to determine whether the quadrilateral with the given vertices forms a parallelogram. If it is a parallelogram, determine whether it is also a rhombus.
$- 11 x + 1.1 = - 36.9 - 1.5 x$

A) $\{ - 47 \}$
B) $\{ 4 \}$
C) $\{ 3.6 \}$
D) $\{ 3.5 \}$

Answer 1

B

Question 2

Use slope to determine whether the quadrilateral with the given vertices forms a parallelogram. If it is a parallelogram, determine whether it is also a rhombus.
-35 - 3x = -10 + 2x A) $\{ - 7 \}$
B) $\{ - 5 \}$
C) $\{ 5 \}$
D) $\{ 7 \}$

Answer 2

B

Question 3

Use slope to determine whether the quadrilateral with the given vertices forms a parallelogram. If it is a parallelogram, determine whether it is also a rhombus.
5(x + 2)= 6(x - 3) A) $\{ - 8 \}$
B) $\{ 6 \}$
C) $\{ 28 \}$
D) $\{ - 28 \}$

Answer 3

C

Question 4

Use slope to determine whether the quadrilateral with the given vertices forms a parallelogram. If it is a parallelogram, determine whether it is also a rhombus.
9x - (3x - 1)= 2 A) $\left\{ \frac { 1 } { 12 } \right\}$
B) $\left\{ \frac { 1 } { 6 } \right\}$
C) $\left\{ - \frac { 1 } { 6 } \right\}$
D) $\left\{ - \frac { 1 } { 12 } \right\}$

Question 5

Use slope to determine whether the quadrilateral with the given vertices forms a parallelogram. If it is a parallelogram, determine whether it is also a rhombus.
$0.10 ( 70 ) + 0.70 x = 0.40 ( 70 + x )$

A) $\{ 80 \}$
B) $\{ 35 \}$
C) $\{ 60 \}$
D) $\{ 70 \}$

Question 6

Determine whether the equation is linear or nonlinear.
$$\sqrt { 5 } x + 3 = 0$$

A)linear
B)nonlinear

Question 7

Use slope to determine whether the quadrilateral with the given vertices forms a parallelogram. If it is a parallelogram, determine whether it is also a rhombus.
-4x - 20 = -2x - 4 A) $\{ 10 \}$
В) $\{ - 10 \}$
C) $\{ - 8 \}$
D) $\{ 8 \}$

Question 8

Use slope to determine whether the quadrilateral with the given vertices forms a parallelogram. If it is a parallelogram, determine whether it is also a rhombus.
$$\frac { 1 } { 2 } x - 1 = \frac { 1 } { 3 } x - 6$$

A) $\left\{ \frac { 5 } { 6 } \right\}$
B) $\{ 30 \}$
C) $\{ - 30 \}$
D) $\left\{ - \frac { 5 } { 6 } \right\}$

Question 9

Use slope to determine whether the quadrilateral with the given vertices forms a parallelogram. If it is a parallelogram, determine whether it is also a rhombus.
-5x - 2 - 2 = -4(x + 9) A) $\{ 32 \}$
В) $\{ 13 \}$
C) $\{ - 36 \}$
D) $\{ - 32 \}$

Question 10

Determine whether the equation is linear or nonlinear.
$$26 x - \frac { 1 } { 15 } = 19$$

A)linear
B)nonlinear

Question 11

Use slope to determine whether the quadrilateral with the given vertices forms a parallelogram. If it is a parallelogram, determine whether it is also a rhombus.
-4x + 1 - 4(x + 1)= -6x + 1 A) $\left\{ - \frac { 7 } { 4 } \right\}$
B) $\left\{ \frac { 3 } { 5 } \right\}$
C) $\{ - 6 \}$
D) $\{ - 2 \}$

Question 12

Use slope to determine whether the quadrilateral with the given vertices forms a parallelogram. If it is a parallelogram, determine whether it is also a rhombus.
$$0.11 x + 24 = 0.29$$

A)linear
B)nonlinear

Question 13

Use slope to determine whether the quadrilateral with the given vertices forms a parallelogram. If it is a parallelogram, determine whether it is also a rhombus.
16x = -15 + 15x A) $\{ 0 \}$
B) $\{ 15 \}$
C) $\{ - 14 \}$
D) $\{ - 15 \}$

Question 14

Determine whether the equation is linear or nonlinear.
$$\frac { x - 4 } { 7 x + 4 } = 10$$

A)linear
B)nonlinear

Question 15

Use slope to determine whether the quadrilateral with the given vertices forms a parallelogram. If it is a parallelogram, determine whether it is also a rhombus.
4x + 2 = 2x - 16 A) $\{ - 9 \}$
B) $\{ - 8 \}$
C) $\{ 9 \}$
D) $\{ 8 \}$

Question 16

Use slope to determine whether the quadrilateral with the given vertices forms a parallelogram. If it is a parallelogram, determine whether it is also a rhombus.
2(2x - 3)= 3(x + 4) A) $\{ 8 \}$
В) $\{ 18 \}$
C) $\{ - 18 \}$
D) $\{ - 6 \}$

Question 17

Use slope to determine whether the quadrilateral with the given vertices forms a parallelogram. If it is a parallelogram, determine whether it is also a rhombus.
$$\frac { 2 } { 5 } x = 3 + \frac { 1 } { 3 } x$$ A) $\{ - 45 \}$
В) $\{ 45 \}$
C) $\{ 90 \}$
D) $\{ - 90 \}$

Question 18

Determine whether the equation is linear or nonlinear.
$$\frac { 9 } { x } + 1 = 7$$

A)linear
B)nonlinear

Question 19

Determine whether the equation is linear or nonlinear.
$$x ^ { 2 } - 5 = 4$$

A)linear
B)nonlinear

Question 20

Use slope to determine whether the quadrilateral with the given vertices forms a parallelogram. If it is a parallelogram, determine whether it is also a rhombus.
$$\frac { - 3 x + 5 } { 2 } + 1 = - \frac { 6 x } { 7 }$$

A) $\left\{ \frac { 7 } { 3 } \right\}$
B) $\left\{ \frac { 49 } { 33 } \right\}$
C) $\left\{ \frac { 49 } { 9 } \right\}$
D) $\left\{ - \frac { 7 } { 3 } \right\}$

Question 21

Solve the equation.
The product of 6 and a number, increased by 3, is 21.

A)6x + 3 = 21
B)18x = 21
C)6(x + 3)= 21
D)6x - 3 = 21

Question 22

Solve the equation.
Three times a number is equal to 20 decreased by the number.

A)3x = x - 20
B)3x = 20 - x
C)3 + x = 20 - x
D)3x = 20 + x

Question 23

Use slope to determine whether the quadrilateral with the given vertices forms a parallelogram. If it is a parallelogram, determine whether it is also a rhombus.
x(5x - 1)= (5x + 1)(x - 3) A) $\left\{ - \frac { 3 } { 14 } \right\}$
В) $\left\{ - \frac { 3 } { 4 } \right\}$
C) $\{ 2 \}$
D) $\left\{ - \frac { 3 } { 13 } \right\}$

Question 24

Use slope to determine whether the quadrilateral with the given vertices forms a parallelogram. If it is a parallelogram, determine whether it is also a rhombus.
$$x \left( x ^ { 2 } + 8 \right) = 3 + x ^ { 3 }$$

A) $\left\{ \frac { 3 } { 8 } \right\}$
B) $\{ 3 \}$
C) $\{ 8 \}$
D) $\left\{ \frac { 8 } { 3 } \right\}$

Question 25

Use slope to determine whether the quadrilateral with the given vertices forms a parallelogram. If it is a parallelogram, determine whether it is also a rhombus.
$$\frac { 6 } { x + 4 } - \frac { 8 } { x - 4 } = \frac { 8 } { x ^ { 2 } - 16 }$$

A) $\{ 2 \sqrt { 14 } \}$
B) $\{ 64 \}$
C) $\{ - 32 \}$
D) $\{ 32 \}$

Question 26

Use slope to determine whether the quadrilateral with the given vertices forms a parallelogram. If it is a parallelogram, determine whether it is also a rhombus.
0.50x - 0.20(20 + x)= 1.00(20) A) $\{ 70 \}$
B) $\{ 40 \}$
C) $\{ 80 \}$
D) $\{ 90 \}$

Question 27

Use slope to determine whether the quadrilateral with the given vertices forms a parallelogram. If it is a parallelogram, determine whether it is also a rhombus.
$$\frac { x } { x - 4 } - 4 = \frac { 4 } { x - 4 }$$

A) $\{ 4 , - 4 \}$
B) $\{ 4 \}$
C) no solution
D) $\{ - 4 \}$

Question 28

Solve the problem.
A rectangular carpet has a perimeter of 288 inches. The length of the carpet is 96 inches more than the width. What are the dimensions of the carpet?

A)132 by 144 in.
B)84 by 108 in.
C)120 by 144 in.
D)120 by 24 in.

Question 29

Solve the equation.
$$\frac { - 3 } { x - 7 } = \frac { 6 } { x - 14 } - \frac { - 21 } { x ^ { 2 } - 21 x + 98 }$$

A) $\{ 7,14 \}$
B) $\{ 14 \}$
C) $\{ 7 \}$
D) no solution

Question 30

Solve the equation.
Three less than 4 times a number equals 17.

A)x - 12 = 17
B)3 - 4x = 17
C)4x 17
D)4x - 3 = 17 3 =

Question 31

Solve the problem.
A bank loaned out $69,000, part of it at the rate of 15% per year and the rest at a rate of 8% per year. If the interest received was $7480, how much was loaned at 15%?

A)$40,000
B)$28,000
C)$29,000
D)$41,000

Question 32

Use slope to determine whether the quadrilateral with the given vertices forms a parallelogram. If it is a parallelogram, determine whether it is also a rhombus.
$$\frac { 2 x } { x ^ { 2 } - 1 } = \frac { 3 } { x ^ { 2 } - 1 } - \frac { 4 } { x + 1 }$$

A) $\left\{ \frac { 1 } { 2 } \right\}$
B) $\left\{ - \frac { 1 } { 8 } \right\}$
C) $\left\{ - \frac { 1 } { 6 } \right\}$
D) $\left\{ \frac { 7 } { 6 } \right\}$

Question 33

Use slope to determine whether the quadrilateral with the given vertices forms a parallelogram. If it is a parallelogram, determine whether it is also a rhombus.
$$( x + 2 ) ( x - 1 ) = ( x + 1 ) ^ { 2 }$$

A) $\{ - 2 \}$
B) $\{ - 3 \}$
C) $\left\{ \frac { 3 } { 2 } \right\}$
D) $\{ 3 \}$

Question 34

Solve the problem.
Center City East Parking Garage has a capacity of 253 cars more than Center City West Parking Garage. If the combined capacity for the two garages is 1219 cars, find the capacity for each garage.

A)Center City East: 483 cars
B)Center City East: 736 cars Center City West: 736 cars Center City West: 483 cars
C)Center City East: 746 cars
D)Center City East: 473 cars Center City West: 473 cars Center City West: 746 cars

Question 35

Solve the problem.
Mary and her brother John collect foreign coins. Mary has four times the number of coins that John has. Together they have 150 foreign coins. Find how many coins Mary has.

A)24 coins
B)120 coins
C)114 coins
D)30 coins

Question 36

Solve the problem.
During an intramural basketball game, Team A scored 19 fewer points than Team B. Together, both teams scored a total of 151 points. How many points did Team A score during the game?

A)66 points
B)67 points
C)85 points
D)75 points

Question 37

Solve the problem.
Don James wants to invest $59,000 to earn $6170 per year. He can invest in B-rated bonds paying 13% per year or in a Certificate of Deposit (CD)paying 7% per year. How much money should be invested in each to realize exactly $6170 in interest per year?

A)$25,000 in B-rated bonds and $34,000 in a CD
B)$35,000 in B-rated bonds and $24,000 in a CD
C)$24,000 in B-rated bonds and $35,000 in a CD
D)$34,000 in B-rated bonds and $25,000 in a CD

Question 38

Solve the equation.
The product of 4 and a number increased by 3 is 20.

A)4x + 3 = 20
B)12x = 20
C)4(x + 3)= 20
D)4x - 3 = 20

Question 39

Solve the equation.
The sum of twice a number and 5 is 9.

A)x + 10 = 9
B)2x + 5 = 9
C)10x = 9
D)2x - 5 = 9

Question 40

Use slope to determine whether the quadrilateral with the given vertices forms a parallelogram. If it is a parallelogram, determine whether it is also a rhombus.
$$\frac { 6 } { 5 x } - \frac { 1 } { x + 1 } = \frac { 3 } { x ( 2 x + 2 ) }$$

A) $\{ 3 \}$
B) $\left\{ \frac { 3 } { 10 } \right\}$
C) $\left\{ \frac { 3 } { 2 } \right\}$
D) no solution

Question 41

Solve the problem.
Two trains leave a train station at the same time. One travels east at 12 miles per hour. The other train travels west at 7 miles per hour. In how many hours will the two trains be 114 miles apart?

A)6.5 hr
B)12 hr
C)3 hr
D)6 hr

Question 42

Solve the problem.
The manager of a candy shop sells chocolate covered peanuts for $6 per pound and chocolate covered cashews for $12 per pound. The manager wishes to mix 80 pounds of the cashews to get a cashew-peanut mixture that will sell for $7 per pound. How many pounds of peanuts should be used?

A)200 lb
B)480 lb
C)240 lb
D)400 lb

Question 43

Solve the problem.
A chemist needs 190 milliliters of a 66% solution but has only 42% and 99% solutions available. Find how many milliliters of each that should be mixed to get the desired solution.

A)80 mL of 42%; 110 mL of 99%
B)110 mL of 42%; 80 mL of 99%
C)70 mL of 42%; 120 mL of 99%
D)120 mL of 42%; 70 mL of 99%

Question 44

Write the power of i as i, -1, -i, or 1.
$( 6 - 7 i ) + ( 3 + 3 i )$

A) $9 + 4 i$
B) $- 9 + 4 \mathrm { i }$
C) $3 + 10 \mathrm { i }$
D) $9 - 4 \mathrm { i }$

Question 45

Solve the problem.
A college student earned $5900 during summer vacation working as a waiter in a popular restaurant. The student invested part of the money at 10% and the rest at 6%. If the student received a total of $478 in interest at the end of the year, how much was invested at 10%?

A)$3100
B)$983
C)$2800
D)$2950

Question 46

Write the sentence as an equation. Let the variable x represent the number.
$$\mathrm { i } ^ { 21 }$$

A)1
B)i
C)-1
D)-i

Question 47

Solve the problem.
Kevin invested part of his $10,000 bonus in a certificate of deposit that paid 6% annual simple interest, and the remainder in a mutual fund that paid 11% annual simple interest. If his total interest for that year was $900, how much did Kevin invest in the mutual fund?

A)$4000
B)$7000
C)$6000
D)$5000

Question 48

Solve the problem.
The owners of a candy store want to sell, for $6 per pound, a mixture of chocolate-covered raisins, which usually sells for $3 per pound, and chocolate-covered macadamia nuts, which usually sells for $8 per pound. They have a 40-pound barrel of the raisins. How many pounds of the nuts should they mix with the barrel of raisins so that they hit their target value of $6 per pound for the mixture?

A)52 lb
B)64 lb
C)56 lb
D)60 lb

Question 49

Solve the problem.
Two cars start from the same point and travel in the same direction. If one car is traveling 59 miles per hour and the other car is traveling at 52 miles per hour, how far apart will they be after 2.1 hours?

A)109.2 mi
B)233.1 mi
C)14.7 mi
D)123.9 mi

Question 50

Write the sentence as an equation. Let the variable x represent the number.
$$\mathrm { i } 8$$

A)1
B)i
C)-i
D)-1

Question 51

Solve the problem.
An airplane flies 450 miles with the wind and 330 against the wind in the same length of time. If the speed of the wind is 20, what is the speed of the airplane in still air?

A)120 mph
B)55 mph
C)130 mph
D)135 mph

Question 52

Solve the problem.
An experienced bank auditor can check a bank's deposits twice as fast as a new auditor. Working together it takes the auditors 4 hours to do the job. How long would it take the experienced auditor working alone?

A)4 hr
B)6 hr
C)8 hr
D)12 hr

Question 53

Solve the problem.
How much pure acid should be mixed with 9 gallons of a 50% acid solution in order to get an 80% acid solution?

A)4.5 gal
B)22.5 gal
C)36 gal
D)13.5 gal

Question 54

Solve the problem.
Two friends decide to meet in Chicago to attend a Cub's baseball game. Rob travels 126 miles in the same time that Carl travels 120 miles. Rob's trip uses more interstate highways and he can average 3 mph more than Carl. What is Rob's average speed?

A)55 mph
B)71 mph
C)60 mph
D)63 mph

Question 55

Write the sentence as an equation. Let the variable x represent the number.
$$\mathrm { i } ^ { 15 }$$

A)-i
B)1
C)i
D)-1

Question 56

Solve the problem.
During a hurricane evacuation from the east coast of Georgia, a family traveled 250 miles west. For part of the trip, they averaged 50 mph, but as the congestion got bad, they had to slow to 30 mph. If the total time of travel was 9 hours, how many miles did they drive at the reduced speed?

A)310 mi
B)300 mi
C)305 mi
D)295 mi

Question 57

Write the power of i as i, -1, -i, or 1.
$$\mathrm { i } ^ { 18 }$$

A)-i
B)1
C)-1
D)i

Question 58

Solve the problem.
The manager of a coffee shop has one type of coffee that sells for $7 per pound and another type that sells for $14 per pound. The manager wishes to mix 90 pounds of the $14 coffee to get a mixture that will sell for $10 per pound. How many pounds of the $7 coffee should be used?

A)60 lb
B)120 lb
C)105 lb
D)210 lb

Question 59

Solve the problem.
BJ can overhaul a boat's diesel inboard engine in 30 hours. His apprentice takes 60 hours to do the same job. How long would it take them working together assuming no gain or loss in efficiency?

A)12 hr
B)90 hr
C)20 hr
D)8 hr

Question 60

Write the sentence as an equation. Let the variable x represent the number.
Tracy can wallpaper 5 rooms in a new house in 15 hours. Together with her trainee they can wallpaper the 5 rooms in 11 hours. How long would it take the trainee working by herself to do the job?

A)35 hr
B)50 hr
C)70 hr
D)15 hr

Question 61

Perform the desired operation. Write the answer in the form a + bi.
$\sqrt { 5 } + 3 \mathrm { i }$

A) $5 + 9 i$
B) 2
C) $5 - 9 \mathrm { i }$
D) 14

Question 62

Write the power of i as i, -1, -i, or 1.
$8 \mathrm { i } + ( - 6 - \mathrm { i } )$

A) $- 6 + 7 i$
B) $- 6 + 9 i$
C) $6 - 9 i$
D) $6 - 7 \mathrm { i }$

Question 63

Write the expression in the standard form a + bi.
$$( 6 + 7 i ) ( 6 - 7 i )$$

A) $- 13$
B) $36 - 49 i ^ { 2 }$
C) 85
D) $36 - 49 \mathrm { i }$

Question 64

Write the expression in the standard form a + bi.
$$( 2 + 8 i ) ( 6 + 6 i )$$

A) $48 \mathrm { i } ^ { 2 } + 60 \mathrm { i } + 12$
B) $60 + 36 i$
C) $- 36 + 60 \mathrm { i }$
D) $- 36 - 60 \mathrm { i }$

Question 65

Write the power of i as i, -1, -i, or 1.
$$( 6 + 6 i ) - ( - 7 + i )$$

A) $- 1 + 7 \mathrm { i }$
B) $13 + 5 i$
C) $13 - 5 \mathrm { i }$
$D ) - 13 - 5 i$

Question 66

Write the expression in the standard form a + bi.
$$( - 4 + 8 i ) ( 4 + i )$$

A) $- 8 - 36 i$
B) $- 24 + 28 i$
C) $- 24 - 36 \mathrm { i }$
D) $- 8 + 28 \mathrm { i }$

Question 67

Perform the desired operation. Write the answer in the form a + bi.
$$( 2 - 3 i ) ^ { 2 }$$

A) $- 5 - 12 \mathrm { i }$
B) $4 - 12 \mathrm { i } + 9 \mathrm { i } ^ { 2 }$
C) $13 - 12 \mathrm { i }$
D) $- 5$

Question 68

Find the product of the given complex number and its conjugate. Write the answer in the form a + bi.
$\frac { 2 } { 2 - 6 i }$

A) $- \frac { 1 } { 8 } + \frac { 3 } { 8 } \mathrm { i }$
B) $- \frac { 1 } { 8 } - \frac { 3 } { 8 } \mathrm { i }$
C) $\frac { 1 } { 10 } + \frac { 3 } { 10 } \mathrm { i }$
D) $\frac { 1 } { 10 } - \frac { 3 } { 10 } \mathrm { i }$

Question 69

Perform the desired operation. Write the answer in the form a + bi.
$\frac { 1 } { 5 } - 2 i$

A) $\frac { 11 } { 5 }$
B) $\frac { 1 } { 25 } + 4 \mathrm { i }$
C) $\frac { 101 } { 25 }$
D) $\frac { 1 } { 25 } - 4 \mathrm { i }$

Question 70

Write the expression in the standard form a + bi.
$$4 \mathrm { i } ( 8 - 5 \mathrm { i } )$$

A) $32 i + 20 i 2$
B) $20 + 32 \mathrm { i }$
C) $32 \mathrm { i } - 20 \mathrm { i } 2$
D) $32 \mathrm { i } - 20$

Question 71

Write the expression in the standard form a + bi.
$$( 8 + 2 \mathrm { i } ) ( 6 - 6 \mathrm { i } )$$

A) $60 - 36 \mathrm { i }$
B) $- 12 i ^ { 2 } - 36 i + 48$
C) $60 + 36 i$
D) $36 + 60 \mathrm { i }$

Question 72

Write the expression in the standard form a + bi.
$$4 ( 8 - 5 i )$$

A) $32 i - 5 i$
B) $8 - 20 \mathrm { i }$
C) $32 - 20 \mathrm { i }$
D) $32 + 20 \mathrm { i }$

Question 73

Find the product of the given complex number and its conjugate. Write the answer in the form a + bi.
$\frac { 4 } { 5 - i }$

A) $\frac { 10 } { 13 } - \frac { 2 } { 13 } \mathrm { i }$
B) $\frac { 10 } { 13 } + \frac { 2 } { 13 } \mathrm { i }$
C) $\frac { 5 } { 6 } + \frac { 1 } { 6 } \mathrm { i }$
D) $\frac { 5 } { 6 } - \frac { 1 } { 6 } \mathrm { i }$

Question 74

Find the product of the given complex number and its conjugate. Write the answer in the form a + bi.
$\frac { 2 i } { 1 - i }$

A) $- 1 - i$
B) $- 1 + 2 i$
C) $- 1 + i$
D) $1 + i$

Question 75

Write the expression in the standard form a + bi.
$$( 5 + 2 i ) ( 5 - 2 i )$$

A) $25 - 4 \mathrm { i } ^ { 2 }$
B) $25 - 4 \mathrm { i }$
C) 29
D) 21

Question 76

Find the product of the given complex number and its conjugate. Write the answer in the form a + bi.
$$\frac { 2 } { 8 + i }$$

A) $\frac { 16 } { 63 } + \frac { 2 } { 63 } \mathrm { i }$
B) $\frac { 16 } { 63 } - \frac { 2 } { 63 } \mathrm { i }$
C) $\frac { 16 } { 65 } + \frac { 2 } { 65 } i$
D) $\frac { 16 } { 65 } - \frac { 2 } { 65 } i$

Question 77

Write the expression in the standard form a + bi.
$8 \mathrm { i } - ( - 3 - \mathrm { i } )$

A) $- 3 + 7 \mathrm { i }$
B) $3 + 9 \mathrm { i }$
C) $3 - 7 \mathrm { i }$
D) $- 3 - 9 \mathrm { i }$

Question 78

Find the product of the given complex number and its conjugate. Write the answer in the form a + bi.
$$\frac { \sqrt { 2 } } { 3 } + \frac { 2 } { 3 } \mathrm { i }$$

A) $\frac { 2 } { 9 } + \frac { 4 } { 9 } \mathrm { i }$
B) $\frac { 4 } { 3 }$
C) $\frac { 2 } { 9 } - \frac { 4 } { 9 } \mathrm { i }$
D) $\frac { 2 } { 3 }$

Question 79

Write the expression in the standard form a + bi.
$$( - 2 + i ) ( - 2 - i )$$

A) $- 2$
B) $- 3$
C) 4
D) 5

Question 80

Write the expression in the standard form a + bi.
$- 3 i ( - 4 + 9 i )$

A) $27 + 12 \mathrm { i }$
B) $12 i - 27 i ^ { 2 }$
C) $- 27 + 12 \mathrm { i }$
D) $12 i + 27 i ^ { 2 }$