1. ## Complex number problem

Hey all here i m having trouble in one more question, it seems simple but i cant seem to get the desired result
any help is greatly appreciated please

If m = cis x & n = cis y, show that m-n/m+n = tan (x-y)/2

2. ## Re: Complex number problem

If you know the exponential notation

$\dfrac{m-n}{m+n}=\dfrac{e^{ix}-e^{iy}}{e^{ix}+e^{iy}}=\dfrac{e^{i(x-y)}-1}{e^{i(x-y)}+1}=\dfrac{e^{i(x-y)/2}-e^{-i(x-y)/2}}{e^{i(x-y)/2}+e^{-i(x-y)/2}}=\\\ldots=i\tan\dfrac{x-y}{2}$