I'm having trouble starting a proof.

I'm supposed to prove that for every z in the set of complex numbers (excluding 0), there exists a w in the set of complex numbers, such that z*w =1. I'm supposed to use the fact that z=a+ib and z* = a-ib = a^2 + b^2. I know that I'm basically proving that there exists a multiplicative inverse for complex numbers. Sorry in advance for my formatting. I don't want help solving the entire proof, just getting started.

Question

I'm having trouble starting a proof. 

I'm supposed to prove that for every z in the set of complex numbers (excluding 0), there exists a w in the set of complex numbers, such that z*w =1.  I'm supposed to use the fact that z=a+ib and z* = a-ib = a^2 + b^2. I know that I'm basically proving that there exists a multiplicative inverse for complex numbers. Sorry in advance for my formatting. I don't want help solving the entire proof, just getting started.

anonymous · Answer

do youknow what the multiplicative inverse of a complex number is?

anonymous · Answer

set $$(a+bi)(c+di)=1$$ and solve for $c, d$ in terms of $a$ and $b$

tiffany_rhodes · Answer

Yes, a/(a^2 + b^2) - b/(a^2 + b^2) i @satellite73

tiffany_rhodes · Answer

Okay, I will try that. Thanks :)