Question 1

Given $z_1 = 2 + 3i$ and $z_2 = 4 - 5i$, what is the product $z_1 	imes z_2$?

Question 2

If $z_1 = 2 + 3i$ and $z_2 = 4 - 5i$, what is the quotient $\frac{z_1}{z_2}$?

Accepted Answer

$\frac{7}{41} + \frac{22}{41}i$

Question 3

Which of the following is the correct formula for multiplying two complex numbers $z_1 = a + bi$ and $z_2 = c + di$?

Accepted Answer

$(ac - bd) + (ad + bc)i$

Question 4

To divide $z_1 = a + bi$ by $z_2 = c + di$, which of the following is the correct formula?

Accepted Answer

$\frac{(ac + bd) + (bc - ad)i}{c^2 + d^2}$

Question 5

A signal in an electrical circuit is represented by the complex number $z = 3 + 4i$. What is the magnitude of this signal?

Accepted Answer

$5$

Question 6

If $z_1 = 1 + 2i$ and $z_2 = 2 - i$, what is $z_1 	imes z_2$?

Question 7

Which of the following is the conjugate of $z = 5 - 7i$?

Accepted Answer

$5 + 7i$

Question 8

A medical imaging device uses the complex number $z = 6 + 8i$ to represent a signal. What is the magnitude of $z$?

Accepted Answer

$10$

Question 9

If $z_1 = 3 + 2i$ and $z_2 = 1 - 4i$, what is $z_1 	imes z_2$?

Accepted Answer

$11 - 10i$

Question 10

Which of the following is the correct result for $\frac{1 + i}{1 - i}$?

Accepted Answer

$i$

Products and Quotients of Complex Numbers

Study Guide - Practice Questions