SOLUTION: The question asks to write the following term into a + ib form, where “i” is a complex number {{{ (sqrt( -1 )) }}}: {{{(1/(x-i y)) }}} Any help would be greatly appreciate

Algebra ->  Complex Numbers Imaginary Numbers Solvers and Lesson -> SOLUTION: The question asks to write the following term into a + ib form, where “i” is a complex number {{{ (sqrt( -1 )) }}}: {{{(1/(x-i y)) }}} Any help would be greatly appreciate      Log On


   



Question 618986: The question asks to write the following term into a + ib form, where “i” is a
complex number +%28sqrt%28+-1++%29%29+:
%281%2F%28x-i+y%29%29+
Any help would be greatly appreciated. Thanks.

Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
The question asks to write the following term into a + ib form, where “i” is a
complex number +%28sqrt%28+-1++%29%29+:
%281%2F%28x-i+y%29%29+
--------------------
Multiply NUM and DEN by the conjugate of the DEN, x + iy
1%2F%28x-i+y%29+=+%28x+%2B+iy%29%2F%28x%5E2+-+i%5E2y%5E2%29
= %28x+%2B+iy%29%2F%28x%5E2+%2B+y%5E2%29
or x%2F%28x%5E2%2By%5E2%29+%2B+i%2A%28y%2F%28x%5E2%2By%5E2%29%29