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OK, let's go back to    sqrt( -4 ) = 2i

Here's what really happened with this problem:

sqrt( -4 ) = sqrt( ( 4 ) ( -1 ) ) = sqrt( 4 ) sqrt( -1 ) = 2i

So...

sqrt( -25 ) = 5i

sqrt( -49 ) = 7i

sqrt( -13 ) = sqrt( 13 ) i
01-complex-numbers-11b.gif
We can't pop the sqrt( 13 ) so we just pull the i out

A complex number is made up of a real number and an imaginary number.

Here are a few:

3 + 2i

-4 + 5i

5/2 - ( sqrt( 3 )/2 ) i

The official form is:

a + bi ... a is the real part and bi is the imaginary part