# Why should one add 180° to the arctan() result of a complex number?

I am now studying phasors and my teacher told us that when you find in an exercise, for example the current and that current is for example $-2 + 3j$ , then, when you want to find the angle, which is $\theta = arctan(-1.5)$, you have to add to the result angle 180 degrees to find the final angle.

My question is, how do I know when to add and when not to add 180 degrees to the angle?

The one-argument arctangent function (atan()) can only return answers in quadrants I and IV. If you know that the point is in quadrant II or III (i.e. the real component is negative) then you need to transform the result via rotation by $\pi$ around the origin.
The two-argument arctangent function (frequently known as atan2()) does not have this caveat.