joudk8147 joudk8147

18-04-2018
Mathematics

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

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sqdancefan sqdancefan

18-04-2018

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°

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