Question

find the principal value of the argument of the complex number
(the principal value lies in range (-pi, pi]

-512-i512*root(3)

I've got the answer as pi/3 but the right answer is 2pi/3, anyone has any idea why?

Answer 1

ops, sorry missed a -
the right answer is -2pi/3

Answer 2

its 2 pi- pi/3 as the number is in third quadrant

Answer 3

that gives 5pi/3 which isn't the answer
why isn't pi/3 enough, it's in the required range

Answer 4

anyone?

Answer 5

let the number be x+iy .
since x<0 and y<0 (x,y) is in the third quadrant
let a be the argument then tan a=|y/x|
but a= -(pi-a)
you can check with a figure

Answer 6

http://www.google.co.in/imgres?q=argument+of+complex+number+third+quadrant&hl=en&sa=X&biw=1440&bih=771&tbm=isch&prmd=ivns&tbnid=zUoW4FS5aIvmmM:&imgrefurl=http://www.xamplified.com/geometrical-to-polar-conversion/&docid=8azrCw5Rh0-SuM&w=261&h=245&ei=mEFSTqCgNIjOrQeLt7DcAQ&zoom=1