Definitions:

The standard form of a complex number is $$a + bi$$ where a and b are real numbers and they can be anything, positive, negative, zero, integers, fractions or decimals.

In the standard form a is called the real part of the complex number and b is called the imaginary part of the complex number and where $$i^2 = -1$$ and $$i = \sqrt{-1}$$

A general example to help you recognize patterns and spot the information you're looking for

$$(2 + i)(3 + i) = 5 + 5i$$ $$6 + 2i + 3i + i^2 = 5 + 5i$$ $$6 + 5i + i^2 = 5 + 5i$$

We use them when we want to explore matrices.

Complex Numbers

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Length: 4:44

Introduction to i and Imaginary Numbers

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Length: 5:20

Calculating i Raised to Arbitrary Exponents

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Length: 6:21

Imaginary Unit Powers »