Question

Find the cube roots of 8(cos 216 + i sin 216)

Answer 1

Well
$$
\Large{
8(cos(216) + i \cdot sin(216)) = 8 \cdot e^{i \cdot 216} \\ \; \\
\sqrt[3]{8 \cdot e^{i \cdot 216}} = \sqrt[3]{8} \cdot \Big(e^{i \cdot 216} \Big)^\frac{1}{3} = 2 \cdot e^{\big(i\frac{216}{3}\big)} = \\
= 2 \cdot e^{i \cdot 72} = 2(cos(72) + i \cdot sin(72))
}
$$

Answer 2

and 2(cos(72)+i⋅sin(72)) is the cube root?

Answer 3

\[2(\cos(72)+i \times(72))\]*

Answer 4

where did the sin() disappear?

Answer 5

oh sorry I forgot to write that

Answer 6

but ye, that's the cube root =]

Answer 7

awesome thanks so much

Answer 8

You're welcome
It is all clear, right?