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Question Number 194847 by cortano12 last updated on 17/Jul/23

$$\underbrace{}$$

Commented by Tinku Tara last updated on 17/Jul/23

$$z=?,\mathrm{without}\mathrm{knowing}z\mathrm{you}\mathrm{cannot}$$$$\mathrm{find}n$$

Commented by Frix last updated on 17/Jul/23

$$n=\frac{19\ln 2}{2\ln z}+\frac{\frac{3\pi }{4}+2k\pi }{\ln z}\mathrm{i}=$$$$=\frac{19\ln 2}{2\ln z}+\frac{(8k+3)\pi }{4\ln z}\mathrm{with}k\in \mathbb{Z}$$$$\iff$$$$z=2^{\frac{19}{2n}}{\mathrm{e}}^{\mathrm{i}\frac{(8k+3)\pi }{4n}}\mathrm{with}k\in \mathbb{Z}\wedge -\frac{4n+3}{8}<k⩽\frac{4n+3}{8}$$

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