solve-z-7-4-

Question Number 165620 by mathlove last updated on 05/Feb/22

s o l v e

z^{7} = - 4

Answered by aleks041103 last updated on 05/Feb/22

z^{7} = - 4 = 4 e^{(2 k + 1) i π}

\Rightarrow z = \sqrt[7]{4} e^{\frac{2 k + 1}{7} i π}, k \in Z

z = \sqrt[7]{4} e^{\frac{i π}{7}}; \sqrt[7]{4} e^{\frac{3 i π}{7}}; \sqrt[7]{4} e^{\frac{5 i π}{7}}; \sqrt[7]{4} e^{i π}; \sqrt[7]{4} e^{\frac{9 i π}{7}}; \sqrt[7]{4} e^{\frac{11 i π}{7}}; \sqrt[7]{4} e^{\frac{13 i π}{7}}