Question and Answers Forum

All Questions      Topic List

Geometry Questions

Previous in All Question      Next in All Question      

Previous in Geometry      Next in Geometry      

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

$$\:\:\:\:\:\:\underbrace{\:} \\ $$

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

z=?, without knowing z you cannot find n

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

Commented by Frix last updated on 17/Jul/23

n=((19ln 2)/(2ln z))+((((3π)/4)+2kπ)/(ln z))i= =((19ln 2)/(2ln z))+(((8k+3)π)/(4ln z)) with k∈Z ⇔ z=2^((19)/(2n)) e^(i(((8k+3)π)/(4n))) with k∈Z ∧ −((4n+3)/8)<k≤((4n+3)/8)

$${n}=\frac{\mathrm{19ln}\:\mathrm{2}}{\mathrm{2ln}\:{z}}+\frac{\frac{\mathrm{3}\pi}{\mathrm{4}}+\mathrm{2}{k}\pi}{\mathrm{ln}\:{z}}\mathrm{i}= \\ $$$$=\frac{\mathrm{19ln}\:\mathrm{2}}{\mathrm{2ln}\:{z}}+\frac{\left(\mathrm{8}{k}+\mathrm{3}\right)\pi}{\mathrm{4ln}\:{z}}\:\mathrm{with}\:{k}\in\mathbb{Z} \\ $$$$\Leftrightarrow \\ $$$${z}=\mathrm{2}^{\frac{\mathrm{19}}{\mathrm{2}{n}}} \mathrm{e}^{\mathrm{i}\frac{\left(\mathrm{8}{k}+\mathrm{3}\right)\pi}{\mathrm{4}{n}}} \:\mathrm{with}\:{k}\in\mathbb{Z}\:\wedge\:−\frac{\mathrm{4}{n}+\mathrm{3}}{\mathrm{8}}<{k}\leqslant\frac{\mathrm{4}{n}+\mathrm{3}}{\mathrm{8}} \\ $$

Terms of Service

Privacy Policy

Contact: info@tinkutara.com