5.4. Complex Numbers

A long time ago, mathematicians were stumped by the following equation:

The reason for this is because any real number (positive or negative) multiplied by itself results in a positive number. How can you multiply any number with itself to get a negative number? No such real number exists. So in the eighteenth century, mathematicians invented something called an imaginary number i (or j— depending what math book you are reading) such that:

Basically a new branch of mathematics was created around this special number (or ...

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