Problem

Find the cube root of
$- 27$
that graphs in the first quadrant.
$3 (\cos [?]^{\circ} + i \sin [?]^{\circ})$

Answer

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Answer

$z = 3 (\cos [60^{\circ}] + i \sin [60^{\circ}])$

Steps

Step 1 ： $z^{3} = - 27$

Step 2 ： $z = - 3 (\cos [180^{\circ}] + i \sin [180^{\circ}])$

Step 3 ： $z = 3 (\cos [60^{\circ}] + i \sin [60^{\circ}])$

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