Question

Find all the cube roots of cube roots le="2 {e}^{2i\pi} " alt="2 {e}^{2i\pi} " align="absmiddle" class="latex-formula">
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Answer 1

Answer:

It is

$1.26{e}^{ \frac{2i\pi}{3}}$

Step-by-step explanation:

$2 {e}^{2i\pi}$

cube root:

$= \sqrt[3]{2 {e}^{2i\pi}} \\ = ( {2 {e}^{2i\pi})}^{ \frac{1}{3} } \\ = {2}^{ \frac{1}{3} } ( {e}^{ \frac{2i\pi}{3} } ) \\ = 1.26{e}^{ \frac{2i\pi}{3}}$