Express the complex number in trigonometric form.-6 + 6 sqrt3 i

Answer:The trigonometric form of the complex number is 12(cos 120° + i sin 120°)Step-by-step explanation:* Lets revise the complex number in Cartesian form and polar form- The complex number in the Cartesian form is a + bi-The complex number in the polar form is r(cosФ + i sinФ)* Lets revise how we can find one from the other- r² = a² + b² - tanФ = b/a* Now lets solve the problem∵ z = -6 + i 6√3∴ a = -6 and b = 6√3∵ r² = a² + b²∴ r² = (-6)² + (6√3)² = 36 + 108 = 144∴ r = √144 = 12∵ tan Ф° = b/a∴ tan Ф = 6√3/-6 = -√3∵ The x-coordinate of the point is negative∵ The y-coordinate of the point is positive∴ The point lies on the 2nd quadrant* The measure of the angle in the 2nd quadrant is 180 - α, where   α is an acute angle∵ tan α = √3∴ α = tan^-1 √3 = 60°∴ Ф = 180° - 60° = 120°∴ z = 12(cos 120° + i sin 120°)* The trigonometric form of the complex number is   12(cos 120° + i sin 120°)