# Complex Principal Argument

• October 13th 2009, 08:58 PM
Fallen186
Complex Principal Argument
Determine the principle value of the argument

-1-i

tan( $\theta$) = -1/-1 = $\frac{\pi}{2}$ but it is negative because it is in the 4th quadrant

the answer is $\frac{-3\pi}{4}$

Principle Argument is simple the argument except between the values of $-\pi$and $\pi$

What did i do wrong?
• October 13th 2009, 09:05 PM
Chris L T521
Quote:

Originally Posted by Fallen186
Determine the principle value of the argument

-1-i

tan( $\theta$) = -1/-1 = $\frac{\pi}{2}$ but it is negative because it is in the 4th quadrant

the answer is $\frac{-3\pi}{4}$

Principle Argument is simple the argument except between the values of $-\pi$and $\pi$

What did i do wrong?

$\tan^{-1}\left(\tfrac{-1}{-1}\right)=\frac{\pi}{4}$.

However, $\theta$ is in the fourth quadrant. So it follows that $\theta=\frac{\pi}{4}-\pi=-\frac{3\pi}{4}$.

Does this make sense?