SOLUTION: If i=square root of -1 and a and b are non-zero real numbers, what is 1/(a+bi)?

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Question 390122: If i=square root of -1 and a and b are non-zero real numbers, what is 1/(a+bi)?
Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!


1%2F%28%28a%2Bbi%29%29

Multiply by the conjugate of the denominator over itself:

expr%281%2F%28%28a%2Bbi%29%29%29expr%28%28%28a-bi%29%29%2F%28%28a-bi%29%29%29+%29

Multiply numerator and denominator:

%28a-bi%29%2F%28%28a%2Bbi%29%28a-bi%29%29

FOIL out the bottom and simplify:

%28a-bi%29%2F%28a%5E2-abi%2Babi-b%5E2i%5E2%29

%28a-bi%29%2F%28a%5E2-b%5E2i%5E2%29

replace iČ by (-1) and simplify:

%28a-bi%29%2F%28a%5E2-b%5E2%28-1%29%29

%28a-bi%29%2F%28a%5E2%2Bb%5E2%29

If you want to write it in the form A+Bi,

%28a%2F%28a%5E2%2Bb%5E2%29%29-%28expr%28b%2F%28a%5E2%2Bb%5E2%29%29%29%2Ai

Edwin