write-z-2-2-3-i-3-in-polar-form-

Question Number 17391 by tawa tawa last updated on 05/Jul/17

write z = {(2 + 2 \sqrt{3} i)}^{3} in polar form .

Answered by ajfour last updated on 05/Jul/17

z = 4^{3} {(\frac{1}{2} + i \frac{\sqrt{3}}{2})}^{3} = 64 {(e^{i π / 3})}^{3}

= {64 e}^{i π} .

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

God bless you sir .

Commented by ajfour last updated on 05/Jul/17

loss of sleep sir . God bless you sir .

Commented by mrW1 last updated on 05/Jul/17

is z = - 64 ?

Commented by b.e.h.i.8.3.4.17@gmail.com last updated on 06/Jul/17

y e s . b e c a u s e o f {E u l e r}^{'} s r u l e :

e^{i π} + 1 = 0 .