Question

the argument of a complex can be found with the following...

Answer 1

\[\cos \theta=\frac{ x }{ |z| } \]
and \[\sin \theta=\frac{ y }{ |z| }\]
for z=x+iy.

Now with z=-2+2i..
when using the\[\cos \theta\] i get argument as \[ \theta=3 pi /4\] and when i use the\[\sin \theta\] I get argument as \[ \theta=pi/4\]...
which is the correct argument?
pi/4 or 3pi/4?

Answer 2

The correct argument is 3pi/4 as the argument of z = -2 + 2i is in the second quadrant (between 90 < theta <= 180 ). The reason why \[\theta \] is pi/4 for sin is that sin is both positive in the first and second quadrant. Furthermore, to know which is the first quadrant like i said before, the complex number is in the second quadrant so it must be between 90 <= \[\theta\] <= 180.

Answer 3

ahh i see it now. thanks a lot.