(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Let a, b in R, not both zero. Find c, d in R such that (a+bi)^-1 = c+di

2. Relevant equations

i^2=-1

R is the set of all real numbers

3. The attempt at a solution

I have a feeling I'm approaching this problem incorrectly but:

1 = (a + bi)(c + di)

=ac + adi + cbi + bdi^2 but i^2=-1

so 1 = ac - bd + (ad + bc)i^2

This is as far as I've attempted becuase I realised that my solution really isn't going anywhere. Maybe someone could just give me a hint to start me off on the right track.

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# Determining Variables Involving Complex Numbers

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