Complex numbers

draw a diagram to see where your number lies

unable or you are not meant to?

if z is in the 1st quadrant, argz = Imz/Rez
if z is in the 2nd quadrant, argz = Imz/Rez +π
if z is in the 3rd quadrant, argz = Imz/Rez - π
if z is in the 4th quadrant, argz = Imz/Rez

(if z is on the axis 0, pi/2, pi, -pi/2, starting with the positive x axis going clockwise)

This is what this particular complex number looks like on the complex plane:

If you can compute the value of $\alpha$, then the argument will be given by $\pi - \alpha$ as you want the angle from the positive half of the real axis.

if it helps write it...
That is how I teach it.

The argument is defined as the angle that is made with the positive real axis. So your angle is pi/2 radians too small!

The definition of argument is the angle between the complex number and the positive part of the real axis. The angle you've specified there is the one between the complex number and the imaginary axis.

Also, by definition, the argument is between $\pi$ and $-\pi$, and so if the complex number was on the other side of the real axis, then the argument would be negative (you didn't make this mistake anywhere, I just thought it would be worth pointing out).

if z is in the 1st quadrant, argz = Imz/Rez
if z is in the 2nd quadrant, argz = Imz/Rez +π
if z is in the 3rd quadrant, argz = Imz/Rez - π
if z is in the 4th quadrant, argz = Imz/Rez

(if z is on the axis 0, pi/2, pi, -pi/2, starting with the positive x axis going clockwise)

Aren't those trigonometric ratios of the angle, not the angle.

You wrote, for example, argz = Imz/Rez.

So the argument of 1+i would be 1/1=1??

You mean tan(argz) = Imz/Rez.

So tan arg(1+i) = 1 meaning arg(1+i) = pi/4

You wrote, for example, argz = Imz/Rez.

So the argument of 1+i would be 1/1=1??

You mean tan(argz) = Imz/Rez.

So tan arg(1+i) = 1 meaning arg(1+i) = pi/4