SOLUTION: Write this expression as a complex number where a,b,c,and d are integers {{{bi/(c+di)}}}

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Question 659314: Write this expression as a complex number where a,b,c,and d are integers
bi%2F%28c%2Bdi%29
Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!
bi%2F%28c%2Bdi%29

Multiply by the unit fraction whose numerator and denominator 
are both the conjugate of the denominator of the given fraction.
 That is, we multiply by %28c-di%29%2F%28c-di%29

bi%2F%28c%2Bdi%29·%28c-di%29%2F%28c-di%29 = %28bi%28c-di%29%29%2F%28%28c%2Bdi%29%28c-di%29%29 = %28bci-bdi%5E2%29%2F%28c%5E2-cdi%2Bcdi-d%5E2i%5E2%29 = %28bci-bdi%5E2%29%2F%28c%5E2-d%5E2i%5E2%29 = 

%28bci-bd%28-1%29%29%2F%28c%5E2-d%5E2%28-1%29%29 = %28bci%2Bbd%29%2F%28c%5E2%2Bd%5E2%29 = bci%2F%28c%5E2%2Bd%5E2%29+bd%2F%28c%5E2%2Bd%5E2%29 = bd%2F%28c%5E2%2Bd%5E2%29+bc%2F%28c%5E2%2Bd%5E2%29i

Edwin