Question

Find all solutions of the equation. leave answers in trigonometric form x^3-8=0 2cis

Answer 1

`x^3-8=0`

`x^3=8=8\mathrm{cis}\,0^\circ`

By DeMoivre's theorem, we have

`x=8^(1/3)\mathrm{cis}\left(\frac{0^\circ+360^\circ k}3\right)`

with
`k=0,1,2`. Then we have three solutions,

`x=2\mathrm{cis}\,0^\circ=2`

`x=2\mathrm{cis}\,120^\circ`

`x=2\mathrm{cis}\,240^\circ`