The argument of a complex number

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Homework Equations

I was just wondering, how do you guys get the argument value from a complex number
without using any calculator, i know that some solutions may be impossible to get without
a calculator but just finding some of the easier angles.

The Attempt at a Solution

Example: If i have the following complex number

z = 1 + sqrt(3)*i

i calculate the absolute value of z (|z|) and since that value is the distance from the origin
to the point (r) i put the value as the hypotenuse of a triangle and apply the x and the y values to the adjecent and the opposite and now i try to find the argument of z.

I use the pythagorean theorem to get the angle of the argument and i get the answer arg(z) = pi / 3 which happens to be true in this case. I'm just wondering if this is the right approach to this problem or if there exist any other probably better solutions for finding the argument of z without the use of a calculator.

//Thx in advance

 

[rock.freak667]

Well that is how you get arg(z). It is the angle measured from the positive real axis to the complex number.