Question 1

Which of the following statements is TRUE about the complex number system?

Accepted Answer

Every real number is also a complex number.

Question 2

What is the standard form of the complex number $-3 + 7i$?

Accepted Answer

$-3 + 7i$

Question 3

Which of the following is a pure imaginary number?

Accepted Answer

$0 + 3i$

Question 4

Simplify the expression $(3 + 5i) + (7 - 9i)$ and write your answer in standard form.

Accepted Answer

$10 - 4i$

Question 5

Subtract $(3 - 10i)$ from $(-8 + 6i)$ and write your answer in standard form.

Accepted Answer

$-11 + 16i$

Question 6

Multiply $(4 + 11i)$ and $(-8 + 3i)$ and write your answer in standard form.

Accepted Answer

$-65 - 76i$

Question 7

What is the value of $\sqrt{-25}$ in terms of $i$?

Accepted Answer

$5i$

Question 8

Solve the equation $x^2 + 49 = 0$ in the complex number system.

Accepted Answer

$x = \pm 7i$

Question 9

Solve the equation $x^2 = -24$ in the complex number system.

Accepted Answer

$x = \pm 2\sqrt{6}i$

Question 10

Which of the following best describes the number $8$ in the context of complex numbers?

Accepted Answer

$8$ is a real number and can be written as $8 + 0i$ in standard form.

Question 11

A medical imaging device uses the solution to $x^2 = -9$ to model certain wave behaviors. What are the solutions in the complex number system?

Accepted Answer

$x = \pm 3i$

Question 12

If $i$ is the imaginary unit, which of the following is TRUE?

Accepted Answer

$i^2 = -1$

Question 13

Solve the quadratic equation $x^2 - 14x + 53 = 0$ in the complex number system.

Accepted Answer

$x = 7 \pm 2i$

Question 14

A chemical process requires you to solve $x^2 = -16$ to determine a reaction's oscillation. What are the solutions?

Accepted Answer

$x = \pm 4i$

Question 15

Which of the following is the correct standard form for the sum $(2 - 3i) + (5 + 4i)$?

Accepted Answer

$7 + i$

Question 16

A physicist is modeling a system using the product $(1 + 2i)(3 - 4i)$. What is the result in standard form?

Accepted Answer

$11 + 2i$

Question 17

Which of the following is NOT a complex number?

Accepted Answer

None of the above; all real and imaginary numbers are complex numbers.

Question 18

Solve for $x$ in the equation $42x^2 + 1 = 8x$ in the complex number system.

Accepted Answer

$x = \frac{8 \pm \sqrt{-128}}{84}$

Question 19

Which of the following best describes the relationship between the sets of real numbers and complex numbers?

Accepted Answer

All real numbers are complex numbers, but not all complex numbers are real numbers.

Question 20

A circuit designer encounters the expression $\sqrt{-49}$. What is the value in terms of $i$?

Accepted Answer

$7i$

Complex Numbers: Definitions, Operations, and Quadratic Equations

Study Guide - Practice Questions