Practice Complex Numbers in Math

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

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.

Example 1

easy
Simplify i^2, i^3, and i^4.

Example 2

medium
Multiply (3 + 2i)(1 - i) and write the result in standard form a + bi.

Example 3

easy
Add (4 + 3i) + (2 - 5i).

Example 4

medium
Simplify i^{23}.