Prove that (where and ).

MATHEMATICS · Subjective · CBSE · Mathematics · Complex Numbers and Quadratic Equations · Complex Numbers and Quadratic Equations

Problem

Prove that tan⁡(iln⁡(a−iba+ib))=2aba2−b2\tan\left(i \ln\left(\frac{a-ib}{a+ib}\right)\right) = \frac{2ab}{a^2-b^2} (where a,b∈R+a, b \in R^+ and i=−1i = \sqrt{-1} ).

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