Counter clock wise vs clock wise angle difference

Question

So today I got my maths exam back. And my teacher didnt gave me mark on this one example. Write this $z=-3$ in polar coordinates and my answer was: $r=3$ and angle=$-180^\circ$. My teacher said that the angle is wrong because we find angle in counter clock wise not in clock wise. But still $-180^\circ$ lands on same results as $180^\circ$ does. Are there any rules which prohibit me to measure angles in clock wise?

Answer 1

It depend on the definition.

I like to define the argument in $[0,2\pi).$

Maybe your teacher gave the similar definition?

Answer 2

If your teacher specified that the principle value of a complex number lies within $(-180,180]$ or $[0,360)$, then he is right. Else you could choose your own interval.

Answer 3

No, your answer isn't technically wrong, but I guess that in class, you would have defined the angle to be in the range $-180^\circ<\theta\le180^\circ$ or $0^\circ\le\theta<360^\circ$, in which case your angle is not correct.