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So it's obvious geometrically that the argument of $z=i$ is $\pi/2$.

However the method of getting the argument is $\arctan(y/x)$. And when in the case of $z=i$, $y/x = 1/0$ which is undefined...

So when you want to find the argument of a complex number is this the correct process -

  1. $\operatorname{Argument}(z) = \arctan(y/x)$ if $x\neq0$.
  2. If $x = 0$, then $\operatorname{Argument}(z) = \pi/2\text{ or }-\pi/2$

Is that the way I should be approaching it?

  • 5
    You will find this [wiki article](http://en.wikipedia.org/wiki/Atan2) very relevant.2012-01-24
  • 2
    Are you sure the arctangent rule is the _definition_ of "argument" in the presentation you're following? That would be unusual; commonly one defines the argument in some different way, and then the arctangent rule is just a _computational_ technique that works if (and only if) the real part is positive.2012-01-24

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