The 2D graph of the complex function z=cos(theta)-isin(theta) is a circle centered at the origin. The direction of the graph is CLOCKWISE.
WHY ?
Hello MohitThe reason is quite straightforward.
$\displaystyle z = \cos\theta \color{red}+\color{black} i\sin\theta$ represent a circle, centre O, in an anticlockwise direction. If we want a circle to go clockwise, we must replace $\displaystyle \theta$ by $\displaystyle -\theta$. Then we get the equation:
$\displaystyle z = \cos(-\theta) + i\sin(-\theta)$
Agreed?
But $\displaystyle \cos(-\theta) = \cos\theta$ and $\displaystyle \sin(-\theta) =-\sin \theta$, so this becomes
$\displaystyle z = \cos\theta - i\sin\theta$
OK?
Grandad