Question 1

Write the expression in the form a + bi, where a and b are real numbers.

Accepted Answer

The answer of Write the expression in the form a...

Question 2

Convert the polar coordinates r = 17,   to rectangular coordinates in the xy-plane. Give the exact answer.

Accepted Answer

The answer of Convert the polar coordinates r = 17,...

Question 3

Convert the polar coordinates r = 6, To rectangular coordinates in the xy-plane.

Accepted Answer

A)  (6, 0) 
B)  (-6, 0) 
C)  (0, 6) 
D)  (0, -6)

Question 4

Write the expression in the form a + bi, where a and b are real numbers. (7 + 6i)³

Accepted Answer

The answer of Write the expression in the form a...

Question 5

Sketch the graph for the polar equation 
  for     .

Accepted Answer

The answer of Sketch the graph for the polar equation...

Question 6

Which of the following alternatives corresponds to (a + bi)2 ?

Accepted Answer

A)  a2 + b2 
B)  a2 + b2i 
C)  (a2 + b2) + (2ab)i 
D)  (a2 - b2) + (2ab)i

Question 7

Convert the polar coordinates r = 5,   to rectangular coordinates in the xy-plane.

Accepted Answer

The answer of Convert the polar coordinates r = 5,...

Question 8

Write 
  in polar form. Give the exact answer using radians for  
 .

Accepted Answer

The answer of Write 
  in polar form. Give...

Question 9

Convert the polar coordinates r = 5,   to rectangular coordinates in the xy-plane. Give the exact answer.

Accepted Answer

The answer of Convert the polar coordinates r = 5,...

Question 10

Convert the rectangular coordinates (-12, -12) to polar coordinates (r, $\theta$). Use radians, and always choose the angle to lie in the interval (-$\pi$, $\pi$]. Give the exact answer.

Accepted Answer

The answer of Convert the rectangular coordinates (-12, -12) to...

Question 11

Write the expression in the form a + bi, where a and b are real numbers.

Accepted Answer

The answer of Write the expression in the form a...

Question 12

Suppose u = (3, -3) and v = (-2, 3). Find u + v.

Accepted Answer

The answer of Suppose u = (3, -3) and v...

Question 13

Evaluate   
 .

Accepted Answer

The answer of Evaluate   
 ....

Question 14

Suppose the wind at airplane heights is 35 miles per hour (relative to the ground) moving 25° north of east. Relative to the wind, an airplane is flying at 350 miles per hour 55° south of the wind. Find the speed and direction of the airplane relative to the ground. Round the speed to 2 decimal places and the angle to the tenth of a degree.

Accepted Answer

The answer of Suppose the wind at airplane heights is...

Question 15

Write the expression in the form a + bi, where a and b are real numbers.

Accepted Answer

A) 
  
B) 
  
C) 
  
D)

Question 16

Convert the polar coordinates r = 17,   to rectangular coordinates in the xy-plane. Give the exact answer.

Accepted Answer

The answer of Convert the polar coordinates r = 17,...

Question 17

Write   in polar form. Give the exact answer using radians for  
 .

Accepted Answer

The answer of Write   in polar form. Give...

Question 18

Let z = a + bi be any complex number such that $z \neq 0$ , then $\frac{1}{z} = \frac{a-bi}{a^2+b^2}$

Accepted Answer

A) True 
 B)False

Question 19

Write   in polar form. Give the exact answer using radians for  
 .

Accepted Answer

The answer of Write   in polar form. Give...

Question 20

Let u and v be vectors. Determine which of the following alternatives is always true.

Accepted Answer

A) 
  
B)   
C) 
  
D)

Exam 8: Polar Coordinates, Vectors, and Complex Numbers

Write the expression in the form a + bi, where a and b are real numbers.

Convert the polar coordinates r = 17, to rectangular coordinates in the xy-plane. Give the exact answer.

Convert the polar coordinates r = 6, To rectangular coordinates in the xy-plane.

Write the expression in the form a + bi, where a and b are real numbers. (7 + 6i)³

Sketch the graph for the polar equation for .

Which of the following alternatives corresponds to (a + bi) ²?

Convert the polar coordinates r = 5, to rectangular coordinates in the xy-plane.

Write in polar form. Give the exact answer using radians for .

Convert the polar coordinates r = 5, to rectangular coordinates in the xy-plane. Give the exact answer.

Convert the rectangular coordinates (-12, -12) to polar coordinates (r, $\theta$ ). Use radians, and always choose the angle to lie in the interval (- $\pi$ , $\pi$ ]. Give the exact answer.

Write the expression in the form a + bi, where a and b are real numbers.

Suppose u = (3, -3) and v = (-2, 3). Find u + v.

Evaluate .

Write the expression in the form a + bi, where a and b are real numbers.

Convert the polar coordinates r = 17, to rectangular coordinates in the xy-plane. Give the exact answer.

Write in polar form. Give the exact answer using radians for .

Let z = a + bi be any complex number such that $z \neq 0$ , then $\frac{1}{z} = \frac{a-bi}{a^2+b^2}$

Write in polar form. Give the exact answer using radians for .

Let u and v be vectors. Determine which of the following alternatives is always true.

Exam 8: Polar Coordinates, Vectors, and Complex Numbers

Write the expression in the form a + bi, where a and b are real numbers.

Convert the polar coordinates r = 17, to rectangular coordinates in the xy-plane. Give the exact answer.

Convert the polar coordinates r = 6, To rectangular coordinates in the xy-plane.

Write the expression in the form a + bi, where a and b are real numbers. (7 + 6i)3

Sketch the graph for the polar equation for .

Which of the following alternatives corresponds to (a + bi) 2 ?

Convert the polar coordinates r = 5, to rectangular coordinates in the xy-plane.

Write in polar form. Give the exact answer using radians for .

Convert the polar coordinates r = 5, to rectangular coordinates in the xy-plane. Give the exact answer.

Convert the rectangular coordinates (-12, -12) to polar coordinates (r, θ\thetaθ ). Use radians, and always choose the angle to lie in the interval (- π\piπ , π\piπ ]. Give the exact answer.

Write the expression in the form a + bi, where a and b are real numbers.

Suppose u = (3, -3) and v = (-2, 3). Find u + v.

Evaluate .

Write the expression in the form a + bi, where a and b are real numbers.

Convert the polar coordinates r = 17, to rectangular coordinates in the xy-plane. Give the exact answer.

Write in polar form. Give the exact answer using radians for .

Let z = a + bi be any complex number such that z≠0z \neq 0z=0 , then 1z=a−bia2+b2\frac{1}{z} = \frac{a-bi}{a^2+b^2}z1​=a2+b2a−bi​

Write in polar form. Give the exact answer using radians for .

Let u and v be vectors. Determine which of the following alternatives is always true.

Write the expression in the form a + bi, where a and b are real numbers. (7 + 6i)³

Which of the following alternatives corresponds to (a + bi) ²?

Convert the rectangular coordinates (-12, -12) to polar coordinates (r, $\theta$ ). Use radians, and always choose the angle to lie in the interval (- $\pi$ , $\pi$ ]. Give the exact answer.

Let z = a + bi be any complex number such that $z \neq 0$ , then $\frac{1}{z} = \frac{a-bi}{a^2+b^2}$