Practice Complex Numbers in Math

Use these practice problems to test your method after reviewing the concept explanation and worked examples.

Worksheet PDF Free Answer-key PDF Family

Quick Recap

Numbers of the form $a + bi$ where $a, b$ are real and $i = \sqrt{-1}$ ; they extend the real numbers to solve $x^2 = -1$ .

Extending numbers into a second dimension to solve equations like $x^2 = -1$ .

Showing a random 20 of 50 problems.

Example 1

medium

Simplify

i^{42}

Example 2

easy

Compute

i^3

Example 3

medium

Solve

x^2 + 16 = 0

over the complex numbers.

Example 4

easy

Add

(4 + 3i) + (2 - 5i)

Example 5

easy

Identify the real and imaginary parts of

4 + 7i

Example 6

medium

Multiply

(2 + i)(3 + 2i)

Example 7

medium

Solve

x^2 - 2x + 5 = 0

over the complex numbers.

Example 8

medium

Compute the modulus

|5 - 12i|

Example 9

hard

|a + bi| = 13

and

a = 5

with

b > 0

, find

b

Example 10

easy

Subtract

(8 - i) - (3 + 4i)

Example 11

medium

Find the product of

z = 5 + 12i

with its conjugate

\bar{z}

Example 12

medium

Compute

(2 + i) + (3 - 4i) - (1 + 2i)

Example 13

medium

Multiply

i\cdot(2 + 3i)

Example 14

medium

Solve

x^2 = -25

over the complex numbers.

Example 15

challenge

Compute

i^{1} + i^2 + i^3 + i^4

Example 16

medium

Simplify

i^{99}

Example 17

easy

What is

i^2

Example 18

medium

Compute

i^{10}

Example 19

easy

Simplify

i^2

i^3

, and

i^4

Example 20

hard

Compute

i + i^2 + i^3 + \cdots + i^{100}

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Related Concepts

Real Numbers Quadratic Formula