Find the real and imaginary parts of log(a+ib)/(a-ib) | Prove that log(a+ib)/(a-ib)=2itan^-1b/a | find the real and imaginary parts of the complex number loga+ib/a-ib

Find the real and imaginary parts of log(a+ib)/(a-ib) | Prove that log(a+ib)/(a-ib)=2itan^-1b/a

find the real and imaginary parts of the complex number

log(\frac{a+ib}{a-ib})

So the real part and the imaginary parts are 0 and 2tan^{-1}\frac{b}{a}