Finding the argument.

[forumguy]

How do you find the argument of -7 - 10i?

[BubbleWrapMan]

Easiest way in this case is to get tan^-1(10/7) since tan(Arg(z)) is equal to Im(z)/Re(z).

However the argument is in the third quadrant, since the number itself is, so subtract pi from the result, so that the angle is between -pi/2 and -pi. The correct quadrant of the angle is something you have to be mindful of.

EDIT: lols wrong ratio

[xZero]

let z=-7-10i
(the gives you the basic angle so you must minus since Arg should be in the third quadrant)

For these type of question always remember , then just convert it to the appropriate quadrant