Powers and Roots of Complex Numbers — Unit test

Question 1

An isosceles triangle’s altitude will bisect its base. Which expression could be used to find the area of the isosceles triangle above?

Revolt · Accepted Answer

StartFraction start root 40 end root . start root 40 end root over 2 EndFraction

Question 2

For two complex numbers z and w, which diagram shows the geometric representation of zw?

Revolt · Accepted Answer

On a coordinate plane, the y-axis is labeled imaginary and the x-axis is labeled real. A line with length r 1 r 2 goes to point z w, a line with length r 1 goes to point z, and a line with length r 2 goes to point w. The angle to line w is theta 2, z is theta 1, z w is theta 1 + theta 2.

Question 3

What are the conjugate and modulus of –14 – 2i?

Revolt · Accepted Answer

–14 + 2i and

Question 4

Review the graph of complex number z.

Revolt · Accepted Answer

(cos(135°) + isin(135°))

Question 5

Consider the polar curve r = 4sin(2θ). What is the length of each petal, and how many petals does the graph have?

Revolt · Accepted Answer

The length of each petal is 4, and the number of petals is 4.

Question 6

Which phrase describes how to divide a complex number z by r(cos θ + i sin θ)?

Revolt · Accepted Answer

Scale by a factor of and rotate clockwise by θ.

Question 7

Review the graph.

Revolt · Accepted Answer

quadrant I

Question 8

A point of the form 25 +bi is 37 units from 13 – 31i. What is the value of b?

Revolt · Accepted Answer

4

Question 9

What is the quotient of ?

Revolt · Accepted Answer

45 (cosine (StartFraction pi Over 6 EndFraction) + I sine (StartFraction pi Over 6 EndFraction) )

Question 10

The following statements are about finding a midpoint of a segment in the complex plane. Which statement is false?

Revolt · Accepted Answer

First subtract the endpoints and then divide by 2.

Powers and Roots of Complex Numbers — Unit test Answers

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