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(Solved): Algebra Q5. Let \( \theta \in \mathbb{R} \) and let \( w=\cos \theta+i \sin \theta \) be a complex ...
Algebra
Q5. Let \( \theta \in \mathbb{R} \) and let \( w=\cos \theta+i \sin \theta \) be a complex number. Prove that if \( w \) is not purely imaginary, then \[ \frac{w^{2}-1}{w^{2}+1}=i \tan \theta \]