1. The problem statement, all variables and given/known data I'm trying to derive the formula for the multiplicative inverse of a complex number. I say that: z=a+bi z-1=u+vi and zz-1 must be 1 so zz-1=(a+bi)(u+vi) =(au-bv)+(av+bu)i =1 So in order for zz-1=1, (au-bv) must be 1 and (av+bu) must be 0. My teacher has solved this as: z-1= a/(a2+b2) - bi/(a2+b2) I just don't know how to get that from au-bv=1 and av+bu=0 2. The attempt at a solution Don't know how to get the last part... major brain fog. Please help?