# Math Help - Argument of a complex number

1. ## Argument of a complex number

Just a quick couple of questions, when working out the argument of a complex number, does the result always have to be between $\pi$ and $-\pi$?

Also, if the number was $1 - i$ for example, is the answer, $\tan^{-1}\frac{-1}{1}$ or $\tan^{-1}\frac{1}{1}$?

Thanks for your help, just forgot a couple of things from earlier in the year

Craig

2. ## Re :

Originally Posted by craig
Just a quick couple of questions, when working out the argument of a complex number, does the result always have to be between $\pi$ and $-\pi$?

Also, if the number was $1 - i$ for example, is the answer, $\tan^{-1}\frac{-1}{1}$ or $\tan^{-1}\frac{1}{1}$?

Thanks for your help, just forgot a couple of things from earlier in the year

Craig

From what i learnt, the angle $\theta$ has to be expressed in radians with domain $-\pi<\theta\leq\pi$ .

The argument for $z=1-i$ is $tan^{-1}\frac{-1}{1}$

remember , for the argument for a complex number z=x+yi , its argument will be $tan^-1\frac{y}{x}$

remember , for the argument for a complex number z=x+yi , its argument will be $\color{red} tan^-1\frac{y}{x}$
That is true only if $x>0$.
Just a quick couple of questions, when working out the argument of a complex number, does the result always have to be between $\pi$ and $-\pi$?
How you define the principle argument is a matter of convention. eg. $0 \leq \theta < 2 \pi$ is equally valid.