Question

How do I find the trigonometric form of the complex number `-1-isqrt3`?

Answer 1

This complex number can be represented graphically as:
To represent it in trigonometric form I first need to calculate the modulus `r` using Pitagora's theorem:
`r=sqrt((-1)^2+(-sqrt(3))^2)=sqrt(1+3)=2`
Then I need to find the angle `theta`;
`theta=pi+arctan(sqrt(3))=4/3pi`
So:
`z=-1-isqrt(3)=2[cos(4/3pi)+isin(4/3pi)]`