Question

The general value of e is given by

• A. $e^{i(\frac{\pi }{2}+2n\pi )\forall nϵ1}$
• B. $e^{-(\frac{\pi }{2}+2n\pi )\forall nϵ1}$
• C. $e^{-i(\frac{\pi }{2}+2n\pi )}\forall nϵ1$
• D. None of these

Answer 1

The correct option is B $e^{-(\frac{\pi }{2}+2n\pi )\forall nϵ1}$

$e=e^{\iota 0}=e^{\cos 2n\pi +\iota \sin 2n\pi }$

$\Rightarrow e^{\iota }=e^{\cos \frac{\pi }{2}+\iota \sin \frac{\pi }{2}}$

$\Rightarrow e^{\iota }=e^{\cos (2n\pi +\frac{\pi }{2})+\iota \sin (2n\pi +\frac{\pi }{2})}$