Complex Numbers Q1

Complex Numbers Q1

It is given that

\(z=\cos\theta+i\sin\theta,\quad0\le\theta<2\pi,\quad\theta\ne\pi.\)

Show clearly that

\(\dfrac{2}{1+z}=1-i\tan(\theta/2).\)

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Answer:\(\dfrac{2}{1+z}=1-i\tan(\theta/2)\) for \(0\le\theta<2\pi,\ \theta\ne\pi\).

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