polar form angles (1 Viewer)

[Riviet]

i just checked that with a question

z = -3 -2i

Arg(z) = tan^-1(2/3)
=33*41'

but if you subract 360 then you get -326*19' which is obviously out of the range -180 < A <= 180

but with what i said...

-(190 - 33*41')
= -146*19'

is in the range AND the correct answer.. just yeah..

My method works only for the angle from 0 clockwise to the angle, your method is straight from whatever angle you have. so 33+180 is the angle from the positive x axis to the |z|, and then you subtract 360 to get -146, it doesn't matter which way you do, as long as answer is right lol.

 

[Dumsum]

With complex numbers the argument is always measured from the positive x-axis, anticlockwise making positive angles and clockwise making negative angles. Looking at your first example, z = 2 - 2i, plot the number in your head. It's in the 4th quadrant, and so -pi/4 is going to be the correct answer. For 3pi/4, the number is going to be z = -2 + 2i (2nd quadrant). Watch your negatives

Basically where you went wrong here:

tan A = 2/-2
-tan A = 1
tan(pi - A) = 1
A = pi - tan^-1(1)
= pi - pi/4
= 3pi/4


is in the 3rd line. -tanA can be tan(pi-A), but it can also be tan(2pi-A), in which case the answer could be 7pi/4, which would be written as -pi/4 to fit into the domain. Just remember: visualise.