Question

dertermine the three cubic roots of 8. give the answer in the form a+bj. also give the main root in the exponential form

Answer 1

If you put 8 into complex polar form raised to the 1/3 power
\[ (8 e^{2\pi i})^{\frac{1}{3}} \]

Answer 2

however, you can substitute \( 2 \pi = 4 \pi = 6 \pi \) for the angle
and you will find 3 unique roots (before finding repeats)

Answer 3

i recall noticing that "3"roots would divide the unit circle into 3 equal parts starting at (8+0i)

then rotating it 120, and another 120 would be the other roots, if im remembering it right

Answer 4

-4+4sqrt(3)i, and -4-4sqrt(3)i .....