convert -1+sqrt3 i into polar form
To convert the complex number -1 + √3i into polar form, we need to find its magnitude (r) and argument (θ).
First, let's find the magnitude (r) using the formula:
|r| = √(a^2 + b^2)
Where a is the real part (-1) and b is the imaginary part (√3):
|r| = √((-1)^2 + (√3)^2)
|r| = √(1 + 3)
|r| = √4
|r| = 2
Next, let's find the argument (θ) using the formula:
θ = arctan(b/a)
θ = arctan(√3 / -1)
θ = arctan(-√3)
θ ≈ -π/3 (approximately -1.047)
Therefore, the polar form of -1 + √3i is 2∠(-π/3) or 2∠-1.047 radians.