ATAR Notes: Forum

VCE Stuff => VCE Mathematics => VCE Mathematics/Science/Technology => VCE Subjects + Help => VCE Specialist Mathematics => Topic started by: forumguy on February 27, 2011, 04:20:42 pm

Title: Finding the argument.
Post by: forumguy on February 27, 2011, 04:20:42 pm: How do you find the argument of -7 - 10i?
Title: Re: Finding the argument.
Post by: BubbleWrapMan on February 27, 2011, 04:31:14 pm: 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
Title: Re: Finding the argument.
Post by: xZero on February 27, 2011, 04:31:33 pm: let z=-7-10i
$Arg(z)=(tan^-1(\frac{-10}{-7}) - \pi)$ (the $tan^-1$ gives you the basic angle so you must minus $\pi$ since Arg should be in the third quadrant)

For these type of question always remember $Arg(z)=tan^1(\frac{y}{x})$ , then just convert it to the appropriate quadrant