Find all cube roots of 64 (cos 219 degrees +i sin 219 degrees)

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asked Oct 16, 2019 194k views

1 Answer

Memius · Answer 1 · 2019-10-22T03:33:37+0000

The principal root is
(64∠219°)^(1/3) = (64)^(1/3)∠(219°/3) = 4∠73°

The other two roots are 120° and 240° from this, so the three roots are
4∠73°
4∠193°
4∠313°

Find all cube roots of 64 (cos 219 degrees +i sin 219 degrees)

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