Question 1

Let   Be a complex number. Find

Accepted Answer

A) 
   
B) 
  
C) 
   
D) 
   
A) 
   
B) 
  
C) 
   
D) 
   A

Question 2

Convert the rectangular coordinates (3, 1) 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 (3, 1) to...

Question 3

Suppose u = (-3, 4) and v = (5, -2).
A) Draw a figure illustrating the difference of u and v as arrows.
B) Compute the sum u - v using coordinates.

Accepted Answer

Part A:
   
Part B: (-8, 6)

Question 4

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 5

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

Accepted Answer

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

Question 6

Sketch the graph for the polar equation 
   for    .

Accepted Answer

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

Question 7

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 8

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

Accepted Answer

A) 
   
B) 
   
C) 
   
D) 
   
A) 
   
B) 
   
C) 
   
D)

Question 9

Suppose u = (2, 1) and v = (3, 1). Compute    .

Accepted Answer

The answer of Suppose u = (2, 1) and v...

Question 10

Evaluate    
 .

Accepted Answer

The answer of Evaluate    
 ....

Question 11

Suppose v = (a , b) and    . Which of the following vectors have magnitude 5?

Accepted Answer

A)  (b, a) 
B)  (-b, -a) 
C)  (-a, -b) 
D)  All of them 
A)  (b, a) 
B)  (-b, -a) 
C)  (-a, -b) 
D)  All of them

Question 12

Write the expression in the form a + bi, where a and b are real numbers. 
(2 + 10i) + (9 + 5i)

Accepted Answer

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

Question 13

Evaluate

Accepted Answer

A) 
   
B) 
   
C) 
   
D) 
   
A) 
   
B) 
   
C) 
   
D)

Question 14

Convert the rectangular coordinates (9, -2) 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 (9, -2) to...

Question 15

The complex number $z = 4^{\frac{1}{6}} \left(-\frac{\sqrt{3}}{2} + \frac{i}{2}\right)$ satisfies the equation $z^6$ = -4

Accepted Answer

A) True 
 B)False

Question 16

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

Accepted Answer

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

Question 17

If z is any complex number, then $z \neq \overline{z}$

Accepted Answer

A) True 
 B)False

Question 18

Convert the rectangular coordinates (-3, 0) to polar coordinates (r, $\pi$). Use radians, and always choose the angle to lie in the interval (- $\pi$,  $\pi$].

Accepted Answer

A) 
  
B) 
  
C) 
  
D) 
  
A) 
  
B) 
  
C) 
  
D)

Question 19

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 20

Sketch the graph for the polar equation 
   for   
 .

Accepted Answer

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

Let Be a complex number. Find

Convert the rectangular coordinates (3, 1) to polar coordinates (r, $\theta$ ). Use radians, and always choose the angle to lie in the interval (- $\pi$ , $\pi$ ]. Give the exact answer.

Suppose u = (-3, 4) and v = (5, -2). A) Draw a figure illustrating the difference of u and v as arrows. B) Compute the sum u - v using coordinates.

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

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

Sketch the graph for the polar equation for .

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

Suppose u = (2, 1) and v = (3, 1). Compute .

Evaluate .

Suppose v = (a , b) and . Which of the following vectors have magnitude 5?

Write the expression in the form a + bi, where a and b are real numbers. (2 + 10i) + (9 + 5i)

Evaluate

Convert the rectangular coordinates (9, -2) to polar coordinates (r, $\theta$ ). Use radians, and always choose the angle to lie in the interval (- $\pi$ , $\pi$ ]. Give the exact answer.

The complex number $z = 4^{\frac{1}{6}} \left(-\frac{\sqrt{3}}{2} + \frac{i}{2}\right)$ satisfies the equation $z^6$ = -4

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

If z is any complex number, then $z \neq \overline{z}$

Convert the rectangular coordinates (-3, 0) to polar coordinates (r, $\pi$ ). Use radians, and always choose the angle to lie in the interval (- $\pi$ , $\pi$ ].

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

Sketch the graph for the polar equation for .

The Real Numbers

Functions and Their Graphs

Linear, Quadratic, Polynomial, and Rational Functions

Exponential Functions, Logarithms, and E

Trigonometric Functions

Trigonometric Algebra and Geometry

Sequences, Series, and Limits

Prelude to Calculus

Filters

Exam 8: Polar Coordinates, Vectors, and Complex Numbers

Let Be a complex number. Find

Convert the rectangular coordinates (3, 1) 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.

Suppose u = (-3, 4) and v = (5, -2). A) Draw a figure illustrating the difference of u and v as arrows. B) Compute the sum u - v using coordinates.

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

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

Sketch the graph for the polar equation for .

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

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

Suppose u = (2, 1) and v = (3, 1). Compute .

Evaluate .

Suppose v = (a , b) and . Which of the following vectors have magnitude 5?

Write the expression in the form a + bi, where a and b are real numbers. (2 + 10i) + (9 + 5i)

Evaluate

Convert the rectangular coordinates (9, -2) 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.

The complex number z=416(−32+i2)z = 4^{\frac{1}{6}} \left(-\frac{\sqrt{3}}{2} + \frac{i}{2}\right)z=461​(−23​​+2i​) satisfies the equation z6z^6z6 = -4

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

If z is any complex number, then z≠z‾z \neq \overline{z}z=z

Convert the rectangular coordinates (-3, 0) to polar coordinates (r, π\piπ ). Use radians, and always choose the angle to lie in the interval (- π\piπ , π\piπ ].

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

Sketch the graph for the polar equation for .

The Real Numbers

Functions and Their Graphs

Linear, Quadratic, Polynomial, and Rational Functions

Exponential Functions, Logarithms, and E

Trigonometric Functions

Trigonometric Algebra and Geometry

Sequences, Series, and Limits

Prelude to Calculus

Filters

Convert the rectangular coordinates (3, 1) to polar coordinates (r, $\theta$ ). Use radians, and always choose the angle to lie in the interval (- $\pi$ , $\pi$ ]. Give the exact answer.

Convert the rectangular coordinates (9, -2) to polar coordinates (r, $\theta$ ). Use radians, and always choose the angle to lie in the interval (- $\pi$ , $\pi$ ]. Give the exact answer.

The complex number $z = 4^{\frac{1}{6}} \left(-\frac{\sqrt{3}}{2} + \frac{i}{2}\right)$ satisfies the equation $z^6$ = -4

If z is any complex number, then $z \neq \overline{z}$

Convert the rectangular coordinates (-3, 0) to polar coordinates (r, $\pi$ ). Use radians, and always choose the angle to lie in the interval (- $\pi$ , $\pi$ ].