If-2x-0i-pii-find-the-value-of-x-

Question Number 92424 by Jidda28 last updated on 06/May/20

If 2 x - 0 i = ϱ^{π i}

find the value of x

Commented by mathmax by abdo last updated on 06/May/20

2 x - o i = e^{π i} \Rightarrow 2 x = - 1 \Rightarrow x = - \frac{1}{2} b e c a u s e e^{i π} = c o s π + i s i n π = - 1

i f w e w a n t a l l s o l u t i o n 2 x = e^{i π + 2 i k π} = e^{i (2 k + 1) π} \Rightarrow

x_{k} = \frac{1}{2} e^{i (2 k + 1) π} k f r o m Z

Commented by Jidda28 last updated on 06/May/20

thank you so much sir

Commented by mathmax by abdo last updated on 07/May/20

y o u a r e w e l c o m e .