SOLUTION: what is the recipical of 7-4i/5

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Question 176897: what is the recipical of 7-4i/5
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
The easy answer is 5%2F%287-4i%29.
Teacher's typically don't like complex numbers in the denominator.
So multiply numerator and denominator by the complex conjugate,

%285%2F%287-4i%29%29%28%287%2B4i%29%2F%287%2B4i%29%29=%2835%2B20i%29%2F%2849%2B16%29
%285%2F%287-4i%29%29%28%287%2B4i%29%2F%287%2B4i%29%29=%2835%2B20i%29%2F%2865%29
%285%2F%287-4i%29%29%28%287%2B4i%29%2F%287%2B4i%29%29=%287%2F13%29%2B%284%2F13%29i
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The reciprocal of (7-4i)/5 is (7/13)+(4/13)i.