Question

cos pi by 6 - i sin pi by 6 divided by 2 into cos pi by 3 + i sin pi by 3​

Answer 1

Answer:

Step-by-step explanation:

Answer 2

Question:

Find the rectangular form of the complex number

$\frac{ \cos(\frac{\pi}{6}) - i \sin( \frac{\pi}{6} ) }{2( \cos( \frac{\pi}{3} ) + </u><u>i</u><u> </u><u>\sin( \frac{\pi}{3} ) }$

Solution

$= \frac{ \cos(\frac{- \pi}{6}) + i \sin( \frac{ -\pi}{6} ) }{2( \cos( \frac{\pi}{3} ) + i\sin( \frac{\pi}{3} ) }$

$= \frac{1}{2} ( \cos( \frac{ - \pi}{6} - \frac{\pi}{3} ) + i \sin( \frac{ - \pi}{6} - \frac{ - \pi}{3} ) ) \\ \\ = \frac{1}{2} ( \cos( \frac{ - 3\pi}{6} ) + i \sin( \frac{ - 3\pi}{6} ) ) \\ \\ = \frac{1}{2} ( \cos( \frac{ - \pi}{2}) + i \sin( \frac{ - \pi}{2} ) ) \\ \\ = \frac{1}{2} ( \cos \frac{\pi}{2} -i \sin \frac{\pi}{2} ) \\ \\ = \frac{1}{2} (0 - i(1)) \\ \\ = \frac{ - i}{2}$

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