solve-the-equation-in-complex-number-z-3-z-o-

Question Number 132937 by mohammad17 last updated on 17/Feb/21

s o l v e t h e e q u a t i o n i n c o m p l e x n u m b e r

z^{3} = z_{o}

Answered by mr W last updated on 17/Feb/21

z_{0} = {r e}^{θ i} = {r e}^{(2 k π + θ) i} w i t h k \in Z

\Rightarrow z = \sqrt[3]{r} e^{(\frac{2 k π}{3} + \frac{θ}{3}) i} w i t h k = 0, 1, 2

Commented by mohammad17 last updated on 17/Feb/21

s i r c a n y o u g i v e m e s t e p s

Commented by mr W last updated on 17/Feb/21

t h e r e i s n o m o r e s t e p . {i t}^{'} s a v e r y b a s i c

t h i n g f o r c o m p l e x n u m b e r s .

w i t h w h a t d o y o u h a v e d i f f i c u l t y ?

(1) w i t h w h y z_{0} = {r e}^{θ i}

(2) w i t h w h y {r e}^{θ i} = {r e}^{(2 k π + θ) i}

(3) w i t h w h y z = \sqrt[3]{r} e^{(\frac{2 k π}{3} + \frac{θ}{3}) i}

(4) w i t h w h y k = 0, 1, 2 a n d n o t k \in Z ?

(5) a l l o f a b o v e

(6) n o n e o f a b o v e

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