Solve-w-3-16-

Question Number 29308 by tawa tawa last updated on 07/Feb/18

Solve : w^{3} = - 16

Answered by Tinkutara last updated on 07/Feb/18

\frac{w^{3}}{- 16} = 1

\frac{w}{- 2^{4 / 3}} = 1, ω, ω^{2}

w = - 2^{4 / 3}, - 2^{4 / 3} ω, - 2^{4 / 3} ω^{2}

Answered by sma3l2996 last updated on 07/Feb/18

w^{3} = - 16 = 16 i^{2} = 16 e^{i π}

w_{k} = 2 \sqrt[3]{2} e^{i (\frac{2 k + 1}{3}) π}

w_{0} = 2 \sqrt[3]{2} e^{i π / 3}; w_{1} = - 2 \sqrt[3]{2}; w_{2} = 2 \sqrt[3]{2} e^{- i π / 3}