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Imaginary Numbers Explained with Formula$ \sqrt{-1} \text{= ?}$What they are and how to simplify
And the Answer is...Imaginary numbers are based around mathematical number i$\text {i is defined to be } \sqrt{-1}$
Imaginary numbers also look like $\sqrt{-3} $ or $ \sqrt{-5}$
We can use the rules for simplifying square roots to rewrite these kinds of imaginary numbers.
$ \sqrt{-a} = \sqrt{-1 \times a} = \sqrt{-1} \times \sqrt{a} = i\sqrt{5} $
A Word Of Caution:
You are probably familiar with the following rule from your work with radicals: However, this rule only works if a > 0 and b > 0. In other words, the product of two radicals does not equal the radical of their products if you are dealing with imaginary numbers.
How to simplify i to any given power:
Calculate the Square Root of:
Simplify
${}$
Imaginary Numbers
Practice Problems Simplify the imaginary numbers below: Problem 1)
Problem 2)
Problem 3)
Problem 4)
Problem 5)
Problem 6)
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