SOLUTION: I am having trouble with this complex number question, finding the reciprocal of this (3-i)/2

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Question 1026767: I am having trouble with this complex number question, finding the reciprocal of this (3-i)/2
Found 2 solutions by macston, MathTherapy:
Answer by macston(5194) About Me  (Show Source):
You can put this solution on YOUR website!
Reciprocal: reverse numerator and denominator:
For (3-i)/2, reciprocal is 2/(3-i).
.
To simplify denominator multiply by conjugate.
Conjugate of (3-i)=(3+i)
.
Reciprocal=%282%2F%283-i%29%29%2A%28%283%2Bi%29%2F%283%2Bi%29%29=%286%2B2i%29%2F%289-%28-1%29%29
Reciprocal=%286%2B2i%29%2F10=6%2F10%2B%282i%29%2F10=%283%2F5%29%2B%28i%2F5%29

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!

I am having trouble with this complex number question, finding the reciprocal of this (3-i)/2
Now that's better. This is much, much clearer now!
%283+-+i%29%2F2
2%2F%283+-+i%29 ------- Reciprocal
%282%283+%2B+i%29%29%2F%28%283+-+i%29%283+%2B+i%29%29 ---- Rationailizing denominator by multiplying fraction by the conjugate of the denominator
2%283+%2B+i%29%2F%289+%2B+3i+-+3i+-+i%5E2%29
2%283+%2B+i%29%2F%289+-+i%5E2%29
2%283+%2B+i%29%2F%289+-+-+1%29 ------ Replacing i%5E2 with - 1
2%283+%2B+i%29%2F10
2%283+%2B+i%29%2F2%285%29
cross%282%29%283+%2B+i%29%2Fcross%282%29%285%29 ------> %283+%2B+i%29%2F5 ------> highlight_green%28matrix%281%2C3%2C+3%2F5%2C+%22%2B%22%2C+%281%2F5%29i%29%29