find-Re-z-and-Im-z-of-e-i-1-2k-pi-1-10-1-1-

Question Number 139027 by mohammad17 last updated on 21/Apr/21

f i n d R e (z) a n d I m (z) o f {[{(e^{i (1 + 2 k) π})}^{\frac{1}{10}} + 1]}^{- 1}

Commented by mohammad17 last updated on 21/Apr/21

? ? ? ?

Answered by MJS_new last updated on 21/Apr/21

e^{i (1 + 2 k) π} = - 1

{(- 1)}^{\frac{1}{10}} = e^{\frac{i π}{10}} = \frac{\sqrt{10 + 2 \sqrt{5}}}{4} - \frac{1 - \sqrt{5}}{4} i

\frac{1}{1 + \frac{\sqrt{10 + 2 \sqrt{5}}}{4} - \frac{1 - \sqrt{5}}{4} i} = \frac{1}{2} + (\frac{1 + \sqrt{5} - \sqrt{5 + 2 \sqrt{5}}}{2}) i

Facebook Tweet Pin