Find-the-cube-root-of-z-1-

Question Number 17392 by tawa tawa last updated on 05/Jul/17

Find the cube root of z = - 1

Answered by mrW1 last updated on 05/Jul/17

- 1

- ω = \frac{1}{2} + \frac{\sqrt{3}}{2} i

- ω^{2} = \frac{1}{2} - \frac{\sqrt{3}}{2} i

Commented by tawa tawa last updated on 05/Jul/17

God bless you sir .

Answered by Arnab Maiti last updated on 07/Jul/17

put x^{3} = z

∴ x^{3} = - 1

or, x^{3} + 1 = 0

or, (x + 1) (x^{2} - x + 1) = 0

∴ (1) x + 1 = 0 \Rightarrow x = - 1

or

(2) x^{2} - x + 1 = 0

∴ x = \frac{1 \pm \sqrt{1 - 4}}{2}

∴ x = \frac{1 \pm i \sqrt{3}}{2} = {\begin{cases} - ω \\ - ω^{2} \end{cases}