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

$$findRe\left(z\right)andIm\left(z\right)ofz={(-2i)}^{-\frac{3}{2}}$$

Answered by MJS_new last updated on 21/Apr/21

$$-2\mathrm{i}={2\mathrm{e}}^{-\frac{\pi }{2}\mathrm{i}}$$$${\left({2\mathrm{e}}^{-\frac{\pi }{2}\mathrm{i}}\right)}^{-\frac{3}{2}}=2^{-\frac{3}{2}}{\mathrm{e}}^{\frac{3\pi }{4}\mathrm{i}}=\frac{\sqrt{2}}{4}(\cos \frac{3\pi }{4}+\mathrm{i}\sin \frac{3\pi }{4})=$$$$=-\frac{1}{4}+\frac{1}{4}\mathrm{i}$$

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