Final answer:
To write the complex number z=-2-2i√3 in trigonometric form, find the magnitude and argument of the complex number.
Step-by-step explanation:
To write the complex number z=-2-2i√3 in trigonometric form, we first need to find the magnitude of the complex number and its argument.
The magnitude of a complex number is given by |z| = √(a^2 + b^2), where a and b are the real and imaginary parts of the complex number respectively. In this case, |z| = √((-2)^2 + (-2√3)^2) = √(4 + 12) = √16 = 4.
The argument (angle) of a complex number is given by θ = tan^(-1)(b/a). In this case, θ = tan^(-1)((-2√3)/(-2)) = tan^(-1)(√3) = 60 degrees.
Therefore, the complex number z=-2-2i√3 can be written in trigonometric form as z=4(cos(60°) + i sin(60°)).