# Math Help - Graph of a complex function?

1. ## Graph of a complex function?

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 ?

2. ## Argand diagram

Hello Mohit
Originally Posted by Mohit
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 ?
The reason is quite straightforward.

$z = \cos\theta \color{red}+\color{black} i\sin\theta$ represent a circle, centre O, in an anticlockwise direction. If we want a circle to go clockwise, we must replace $\theta$ by $-\theta$. Then we get the equation:

$z = \cos(-\theta) + i\sin(-\theta)$

Agreed?

But $\cos(-\theta) = \cos\theta$ and $\sin(-\theta) =-\sin \theta$, so this becomes

$z = \cos\theta - i\sin\theta$

OK?