# Graph of a complex function?

• Apr 23rd 2009, 08:03 PM
Mohit
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 ? (Wondering)
• Apr 24th 2009, 12:15 AM
Argand diagram
Hello Mohit
Quote:

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 ? (Wondering)

The 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?