Question 1

Given two complex numbers $$z_1 = 3 + 2i$ and z_2$ = 1 - 4i$$, what is $$z_1$$ + $$z_2$$?

Accepted Answer

$$4 - 2i$$

Question 2

What is the product of $$(2 + 3i)$$ and $$(1 - 2i)$$?

Accepted Answer

$$8 - i$$

Question 3

Which of the following is the correct formula for the conjugate of a complex number $$z = a + bi$$?

Accepted Answer

$$a - bi$$

Question 4

If $$z = 4 - 5i$$, what is $$z \cdot \overline{z}$$?

Accepted Answer

$$41$$

Question 5

Divide $$(5 + 12i) by$$ $$(3 - 4i)$$ and express your answer in standard form.

Accepted Answer

$$-1 + 4i$$

Question 6

Which of the following is the multiplicative inverse of $$2 + i$$?

Accepted Answer

$$\frac{2 - i}{5}$$

Question 7

If $$z = 7 + 24i$$, what is $$|z|$$?

Accepted Answer

$$25$$

Question 8

Which of the following is the result of multiplying $$(1 + i) by $$itself?

Accepted Answer

$$2i$$

Question 9

A circuit has an impedance of $$3 + 4i$$ ohms. What is the magnitude of the impedance?

Accepted Answer

$$5$$ ohms

Question 10

Which of the following is the correct result for $$(2 - 3i) - (4 + i)$$?

Accepted Answer

$$-2 - 4i$$

Question 11

If $$z = a + bi$$ and $$w = c + di$$, what is the general formula for $$z \cdot w$$?

Accepted Answer

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

Question 12

Which of the following is the additive inverse of $$-6 + 8i$$?

Accepted Answer

$$6 - 8i$$

Question 13

If $$z = 2 + 5i$$, what is the real part of $$z$$?

Accepted Answer

$$2$$

Question 14

Which of the following is the result of dividing $$1 by$$ $$i$$?

Accepted Answer

$$-i$$

Question 15

If $$z = 3 + 4i$$, what is $$\overline{z}$$?

Accepted Answer

$$3 - 4i$$

Sums, Products, and Quotients of Complex Numbers

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