Using Complex Numbers to Deduce Trigonometric Values Q1

Using Complex Numbers to Deduce Trigonometric Values Q1

TGM Original Questions

Evaluate the product \((1+\mathbf{i})(1+\sqrt{3}\mathbf{i})\).

Hence, deduce that \(\tan \left( \frac{7\pi }{12} \right)=-(2+\sqrt{3})\).

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Answer:\(\text{Product:}\hspace{0.5em}(1-\sqrt{3})+(1+\sqrt{3})\mathbf{i}\) \(\text{Hence:}\hspace{0.5em}\tan\left(\dfrac{7\pi}{12}\right)=-(2+\sqrt{3})\)

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