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)

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- Apr 23rd 2009, 08:03 PMMohitGraph 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 AMGrandadArgand diagram
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 - Apr 25th 2009, 07:45 PMMohit
thx, i understand