SOLUTION: how can I solve this problem? 2i ______ 1-i

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Question 171035: how can I solve this problem?
2i
______
1-i
Answer by gonzo(654) About Me  (Show Source):
You can put this solution on YOUR website!
you need to remove the 1-i from the denominator.
here's how:
multiply numerator and denominator by (1+i)
your equation becomes:
%282i%2A%281%2Bi%29%29%2F%28%281-i%29%2A%281%2Bi%29%29
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when you multiply %281-i%29%2A%281%2Bi%29 you get:
1+-+i+%2B+i+-+i%5E2
which becomes:
1+-+i%5E2
since i%5E2+=+-1, it becomes:
1+-+%28-1%29
which becomes:
2
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the denominator of your equation is 2
the numerator is:
2i%2A%281%2Bi%29
when you multiply that out, you get:
2i+%2B+2i%5E2
since i^2 = -1, that becomes:
2i+%2B+2%2A%28-1%29
which becomes
2i+-2
your equation is now:
%282i-2%29%2F2
simplify by dividing the numerator by the denominator to get:
i-1
put in standard complex form with the real part first and the imaginary part last:
-1%2Bi
and you're done.
the answer is:
-1%2Bi