SOLUTION: what is the multiplicative inverse of 3+5i 8

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Question 420562: what is the multiplicative inverse of
3+5i
8
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
I'm a little confused by the 8? I'm assuming that it is a typo.

The multiplicative inverse of 3+5i is what you misgh expect it to be:
1%2F%283%2B5i%29
However this is not the proper form. We want something in the standard form:
a + bi
where a and b are real numbers.

To put
Multiplying the numerator is simple. To multiply the denominator we can use FOIL or the %28a%2Bb%29%28a-b%29+=+a%5E2-b%5E2 pattern. I prefer using the pattern:
%283-5i%29%2F%28%283%29%5E2-%285i%29%5E2%29
which simplifies as follows:
%283-5i%29%2F%289-25i%5E2%29
%283-5i%29%2F%289-25%28-1%29%29 (since i%5E2+=+-1)
%283-5i%29%2F%289%2B25%29
%283-5i%29%2F34
For standard form we need to split up this fraction:
3%2F34%2B+%28-5i%29%2F34
or
3%2F34%2B+%28%28-5%29%2F34%29i