prove-that-e-i-e-i-2k-given-that-k-0-1-2-

Question Number 70138 by Scientist0000001 last updated on 01/Oct/19

p r o v e t h a t e^{i θ} = e^{i (θ + 2 k Π)} g i v e n t h a t k = 0, \pm 1, \pm 2 \dots

Answered by mind is power last updated on 01/Oct/19

e^{i x} = c o s (x) + i s i n (x)

\Rightarrow e^{i (θ + 2 k π)} = c o s (θ + 2 k π) + i s i n (2 k π + θ)

= c o s (θ) + i s i n (θ) w e u s e d p e r i o d i c i t y o f S i n a n d v o s w i t c h i s 2 π

c o s (θ) + i s i n (θ) = e^{i θ}