The imaginary unit i is the principal square root of -1, that is, i=-1. From this definition, it can also be said that i2=-1.
Imaginary Unit i=-1 or i2=-1
The imaginary unit i can also be regarded as a solution to the equationx2+1=0.
x2+1=0⇒i2+1=0
The imaginary unit allows to rewrite the square root of any negative number. Once i replaces the square root of -1, the square root of the remaining positive number can be evaluated as usual.
-a=a⋅-1=a⋅i
The above property is true only when a>0. Here are some examples of how to use the property to simplify radical expressions.
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