Question

How do you find the principle argument of `4(-cos(pi/3)+isin(pi/3))`?

Answer 1

Argument is `(2pi)/3`.

Explanation:

Observe `4(-cos(pi/3)+isin(pi/3))`. In it while real portion `-4cos(pi/3)` is negative, imaginary portion `4isin(pi/3)` is positive and hence in a complexnumber plane, the number will appear in second quadrant.

Hence, wecan write `4(-cos(pi/3)+isin(pi/3))`

as `4(cos(pi-pi/3)+isin(pi-pi/3))`

or `4(cos((2pi)/3)+isin((2pi)/3))`

Hence, while modulus is `4`, argument is `(2pi)/3`.