ISRO 2012: [Mech] Complex Numbers

Question

1+ i Is equivalent to

(a) √ 2  $e ^{- i π /4 }$

(b) √ 2  $e^ {i π /4}$

(c) 2  $e^ {- i π /4}$
(d) 2  $e^ {i π /4}$

Answer 1

$e^{i\Theta} = cos\Theta + i*sin\Theta.$

$\therefore 1+i=\sqrt2*(1/{\sqrt2}+i/\sqrt2)$

$=\sqrt2 e^{i\pi/4}$