find-Re-z-and-Im-z-of-z-2i-3-2-

Question Number 139023 by mohammad17 last updated on 21/Apr/21

f i n d R e (z) a n d I m (z) o f z = {(- 2 i)}^{- \frac{3}{2}}

Answered by MJS_new last updated on 21/Apr/21

- 2 i = {2 e}^{- \frac{π}{2} i}

{({2 e}^{- \frac{π}{2} i})}^{- \frac{3}{2}} = 2^{- \frac{3}{2}} e^{\frac{3 π}{4} i} = \frac{\sqrt{2}}{4} (\cos \frac{3 π}{4} + i \sin \frac{3 π}{4}) =

= - \frac{1}{4} + \frac{1}{4} i

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