SOLUTION: Find the multiplicative inverse of each complex number. 4-2i

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Question 27317: Find the multiplicative inverse of each complex number. 4-2i
Answer by bmauger(101) About Me  (Show Source):
You can put this solution on YOUR website!
Multiplicative inverse means that when you multiply it by the number you'll get one, so what you're essentially doing is solving for is x in this equation:
%284-2i%29x=1
x=1%2F%284-2i%29
However you can't leave an i value in the bottom of the equation, so you have to multiply the top & bottom by 4+2i.
x=%281%2F%284-2i%29%29%2A%28%284%2B2i%29%2F%284%2B2i%29%29
x=%284%2B2i%29%2F%2816-4i%5E2%29Since i%5E2=-1:
x=%284%2B2i%29%2F%2820%29
In other words, dividing by (4-2i) is the same thing as multiplying by (4+2i)/20.