Complex Principal Argument

**Fallen186** · October 13th 2009, 08:58 PM

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?

**Chris L T521** · October 13th 2009, 09:05 PM

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?

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