Proving Trigonometric Ratios by Complex Numbers Q1

Proving Trigonometric Ratios by Complex Numbers Q1

Evaluate the product \((1+i)(1+\sqrt{3}i)\). Deduce that \(\tan \left( \frac{7\pi }{12} \right)=-(2+\sqrt{3})\).

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Answer:\((1+i)(1+\sqrt3i)=(1-\sqrt3)+(1+\sqrt3)i\) \(\tan\frac{7\pi}{12}=-(2+\sqrt3)\)

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