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Imaginary Numbers

What in the heck are imaginary numbers? If you have ever come across the letter i, then you have come across an imaginary number. If you have worked through a problem and got a negative number under a radical sign, you have come across an imaginary number. So, let's take a look at these numbers, shall we?

imaginarynumbersdefinition
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If we look at this definition from a mathematical standpoint, then…

imaginarynumbers1

and if that's the case, then…

imaginarynumbers2
Can we re-write imaginary numbers?

Absolutely! In fact, since you have already learned some rules from working with radicals, just apply the same rules here! It's quite easy. You know how you simplify square roots? Do the same thing with the imaginary number! Check it out.

imaginarynumbers3

This means the rule for working with imaginary numbers looks like this!

ruleforrewritingimaginarynumbers

IMPORTANT! Keep in mind that the radical rule

imaginarynumbers4

only works when a > 0 and b > 0. In other words, the product of two radicals does NOT equal the radical of their products when you are working with imaginary numbers

©2011–2017 Sherry Skipper Spurgeon.

All Rights Reserved.

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