Question

(cos5π/6+isin5π/6)^2​

Answer 1

Answer:

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Answer 2

Step-by-step explanation:

We have,

$( \cos( \frac{5\pi}{6} ) + i \sin( \frac{5\pi}{6} ) ) ^{2}$

From euler's formula,

${e}^{i \theta} = \cos( \theta) + i \sin( \theta)$

so,

$( \cos( \frac{5\pi}{6} ) + i \sin( \frac{5\pi}{6} ) ) ^{2} = {( {e}^{ \frac{5\pi}{6} i} })^{2}$

$= {e}^{ \frac{10\pi}{6} i}$

$= {e}^{ \frac{5\pi}{3}i }$

$= {e}^{(2\pi - \frac{\pi}{3} )i}$

$= \cos(2\pi - \frac{\pi}{3} ) + i \sin(2\pi - \frac{\pi}{3} )$

$= \cos( \frac{\pi}{3} ) - i \sin( \frac{\pi}{3} )$

$= \frac{1}{2} - i\frac{ \sqrt{3} }{2}$

$= \frac{1 - i \sqrt{3} }{2}$