Question #347965

If z=8(cos5π3+isin5π3)8(\cos \frac{5\pi}{3}+i\sin \frac{5\pi}{3}), then z6 is equal to


1
Expert's answer
2022-06-06T16:53:20-0400
z6=86(cos(6(5π3))+isin(6(5π3)))z^6=8^6\big(\cos(6(\dfrac{5\pi}{3}))+i\sin(6(\dfrac{5\pi}{3}))\big)

=262144(cos(10π)+isin(10π))=262144=262144\big(\cos(10\pi)+i\sin(10\pi)\big)=262144


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