-1+root3i
turn that into rcis angle
the angle is 2pi/3 but i dont know hwy
To convert a complex number into its polar form (rcisθ), where r is the magnitude and θ is the angle, we need to calculate the magnitude and the angle.
Given that -1 + √3i is a complex number, we can calculate its magnitude:
|r| = sqrt((-1)^2 + (√3)^2)
|r| = sqrt(1 + 3)
|r| = sqrt(4)
|r| = 2
To find the angle, we can use the inverse tangent function:
θ = atan(√3 / -1)
θ = atan(-√3)
However, this gives us the angle in the fourth quadrant. Since we want the angle in the standard position (between 0 and 2π), we can add 2π to the angle to obtain:
θ = atan(-√3) + 2π
Therefore, the complex number -1 + √3i in polar form (rcisθ) is 2cis(atan(-√3) + 2π), or simply 2cis(2π/3).