SOLUTION: how to solve with Given that (x+iy)/(2-i) , find x and y.

Algebra ->  Complex Numbers Imaginary Numbers Solvers and Lesson -> SOLUTION: how to solve with Given that (x+iy)/(2-i) , find x and y.      Log On


   



Question 266600: how to solve with Given that (x+iy)/(2-i) , find x and y.
Answer by drk(1908) About Me  (Show Source):
You can put this solution on YOUR website!
we are given
(i) %28x%2Biy%29%2F%282-i%29
step 1 - multiply by the conjugate of (2-i) which is (2+i) to get
(ii) %28%28x%2Biy%29%282%2Bi%29%29%2F%28%282-i%29%282%2Bi%29%29
and simplified, we get
(iii) %282x+%2B+xi+%2B+2iy+-+y%29%2F5
we then separate our real and imaginary parts to get
(iv) %282x-y%29%2F5 + %28%28x%2B2y%29%2Ai%29%2F5
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at this point there is no equal sign, so we can't solve for x and y, just rewrite using x and y in the real and imaginary parts.