Question 1

Which of the following is the correct definition of the imaginary unit $i$?

Accepted Answer

$i = \sqrt{-1}$

Question 2

What is the standard form of a complex number?

Accepted Answer

$a + bi$, where $a$ and $b$ are real numbers

Question 3

Which of the following is the result of $\sqrt{-48}$ expressed in terms of $i$?

Accepted Answer

$4i\sqrt{3}$

Question 4

If $z_1 = 3 - 4i$ and $z_2 = 2 + 6i$, what is $z_1 + z_2$?

Accepted Answer

$5 + 2i$

Question 5

What is the result of multiplying $(2 - 3i)(3 + 4i)$?

Accepted Answer

$18 + i$

Question 6

Which of the following is the conjugate of the complex number $6 + 5i$?

Accepted Answer

$6 - 5i$

Question 7

What is the result of dividing $3 + 2i$ by $5 - i$ in standard form $a + bi$?

Accepted Answer

$\frac{13}{26} + \frac{11}{26}i$

Question 8

Simplify $i^{15}$.

Accepted Answer

$i$

Question 9

Which of the following statements is true about the product of a complex number and its conjugate?

Accepted Answer

The product is always a real number

Question 10

A medical imaging device uses the complex number $z = 4 - 3i$ to represent a signal. What is the modulus (absolute value) of $z$?

Accepted Answer

$5$

Question 11

Which of the following is the result of $\sqrt{-20} \div \sqrt{-2}$?

Accepted Answer

$\sqrt{10}$

Question 12

If $a = 0$ and $b 
eq 0$, the complex number $a + bi$ is called a(n) ________ number.

Accepted Answer

pure imaginary

Question 13

Which of the following is the correct simplification of $\frac{8 + \sqrt{-128}}{4}$ in standard form $a + bi$?

Accepted Answer

$2 + 2i\sqrt{2}$

Question 14

Which property is used when adding complex numbers $a + bi$ and $c + di$?

Accepted Answer

Add real parts and add imaginary parts

Question 15

A chemical reaction is modeled by the complex number $z = 2 + 4i$. What is the argument (angle) $	heta$ of $z$ in radians?

Accepted Answer

$\arctan(4/2)$

Question 16

Which of the following is the correct result of $(3 + 2i) + (9 - 3i)$?

Accepted Answer

$12 - i$

Question 17

Simplify $i^{23}$.

Accepted Answer

$-i$

Question 18

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

Accepted Answer

$13$

Question 19

A complex number $z$ is equal to its conjugate only if:

Accepted Answer

Its imaginary part is zero

Question 20

Which of the following is the correct simplification of $\frac{6 + 2i}{1 + 2i}$ in standard form $a + bi$?

Accepted Answer

$2 - i$

Basic Concepts and Operations with Complex Numbers

Study Guide - Practice Questions