Question 1

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

Accepted Answer

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 $$z_2$$?

Accepted Answer

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

스터디 가이드 - 연습 문제