Please help my Math homework 2

Please help my Math homework

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Part 1

(4-3i)(a+ib)=1 where a and b are to be found.

4a+4ib-3ia+3b=1. Therefore 4a+3b=1 and 4b-3a=0, so b=3a/4.

4a+9a/4=1, 25a/4=1, so a=4/25 and b=3/4*4/25=3/25.

The inverse is (4+3i)/25.
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