# Complex Principal Argument

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

-1-i

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

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

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

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

Originally Posted by Fallen186
Determine the principle value of the argument

-1-i

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

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

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

What did i do wrong?

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

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

Does this make sense?