Evaluate- cos- 8 -isin- 8 cos- 8 -isin- 8 4

The correct option is C 1 We know that e^iθ=cosθ+isinθ and e^ 1θ=cosθ isinθ ( cosπ #160; 8 isinπ #160; 8 #160; cosπ #160; ...

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Complex Numbers

Evaluate: c...

Question

Evaluate:
${⎛ ⎜ ⎜ ⎝ \frac{c o s \frac{π}{8} - i s i n \frac{π}{8}}{c o s \frac{π}{8} + i s i n \frac{π}{8}} ⎞ ⎟ ⎟ ⎠}^{4}$

1

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- 1

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2

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\frac{1}{2}

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{(\frac{1 + c o s \frac{π}{8} - i s i n \frac{π}{8}}{1 + c o s \frac{π}{8} + i s i n \frac{π}{8}})}^{8}

{⎛ ⎜ ⎜ ⎝ \frac{1 + cos \frac{π}{8} - i sin \frac{π}{8}}{1 + cos \frac{π}{8} + i sin \frac{π}{8}} ⎞ ⎟ ⎟ ⎠}^{8}

{(\frac{1 + cos \frac{π}{8} - i sin \frac{π}{8}}{1 + cos \frac{π}{8} - i sin \frac{π}{8}})}^{2} =

{⎛ ⎜ ⎜ ⎝ \frac{1 + cos \frac{π}{8} - i sin \frac{π}{8}}{1 + cos \frac{π}{8} + i sin \frac{π}{8}} ⎞ ⎟ ⎟ ⎠}^{8} =

{⎛ ⎜ ⎜ ⎝ \begin{matrix} \frac{1 + cos \frac{π}{8} - i sin \frac{π}{8}}{1 + cos \frac{π}{8} + i sin \frac{π}{8}} \end{matrix} ⎞ ⎟ ⎟ ⎠}^{8}

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