SOLUTION: (2-i)/(-2-i) in standard form

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Question 1091205: (2-i)/(-2-i) in standard form
Answer by Edwin McCravy(20054) About Me  (Show Source):
You can put this solution on YOUR website!
%282-i%29%2F%28-2-i%29 

Multiply by the conjugate of the denominator
over itself, which is just a fraction equal to
1 and  so it will not change the value:

 

Indicate the multiplications of the numerators and
denominators:

%28%282-i%29%28-2%2Bi%29%29%2F%28%28-2-i%29%28-2%2Bi%29%29

Use the "FOIL" process to multiply the binomials
in the top and bottom.

%28-4%2B2i%2B2i-i%5E2%29%2F%284-2i%2B2i-i%5E2%29 

Combine like terms.  Notice that the middle terms cancel
in the bottom, but add together in the top:

%28-4%2B4i-i%5E2%29%2F%284-i%5E2%29

We can always replace i2 by -1

%28-4%2B4i-%28-1%29%29%2F%284-%28-1%29%29

Simplify by changing the -(-1)'s to +1's

%28-4%2B4i%2B1%29%2F%284%2B1%29

Combine like terms

%28-3%2B4i%29%2F5

Write as two fractions, each with the denominator 5.

-3%2F5%2Bexpr%284%2F5%29i

Edwin