SOLUTION: Find the multiplicative inverse of 1/3-i

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Question 1009881: Find the multiplicative inverse of 1/3-i
Found 2 solutions by It is costly, MathLover1:
Answer by It is costly(175) About Me  (Show Source):
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
The multiplicative inverse of a number, +a is 1%2Fa so that
a+%2A%281%2Fa%29+=+1

so, the multiplicative inverse of %281%2F3-i%29 is:
1%2F%281%2F3-i%29+

1%2F%281%2F3-3i%2F3%29+

1%2F%28%281-3i%29%2F3%29+

3%2F%281-3i%29+

3%281%2B3i%29%2F%28%281-3i%29%281%2B3i%29%29+

%283%2B9i%29%2F%281%5E2-%283i%29%5E2%29+

%283%2B9i%29%2F%281-9i%5E2%29+

%283%2B9i%29%2F%281-9%28-1%29%29+

%283%2B9i%29%2F%281%2B9%29+

%283%2B9i%29%2F10+

highlight%283%2F10%2B9i%2F10%29+

check if
%281%2F3-i%29%283%2F10%2B9i%2F10%29=1
%283%2F10%29%281%2F3%29%2B%289i%2F10%29%281%2F3%29-i%283%2F10%29-i%289i%2F10%29=1
%283%2F10%29%281%2F3%29%2B%289i%2F10%29%281%2F3%29-%283i%2F10%29-%289i%5E2%2F10%29=1

%281%2F10%29%2B%283i%2F10%29-%283i%2F10%29-%289i%5E2%2F10%29=1
%281%2F10%29%2Bcross%28%283i%2F10%29%29-cross%28%283i%2F10%29%29-%289%28-1%29%2F10%29=1
%281%2F10%29%2B9%2F10=1
10%2F10=1
1=1