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dsp73
2 years ago
14

PLEASE PLEASE HELP!!!!

Mathematics
1 answer:
Usimov [2.4K]2 years ago
6 0

Answer:

B

Step-by-step explanation:

\cos( \alpha )  +  i\sin( \alpha )  =  {e}^{i (\alpha   + 2\pi)}

z = 3(cos π/2 + i sin π/2) =→

3 {e}^{i \frac{\pi}{2} }

z⁷ =

{3}^{7}  {e}^{i \frac{7\pi}{2} }  =   {3}^{7}  {e}^{i \frac{(7 - 4)\pi}{2} }  =  {3}^{7}  {e}^{i \frac{3\pi}{2} }  =  {3}^{7} ( \cos( \frac{3\pi}{2} )  + i \sin( \frac{3\pi}{2} ) ) = 2187( \cos( \frac{3\pi}{2} )  + i \sin( \frac{3\pi}{2} ) )

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