convert -1+sqrt3 i into polar form

Answer 1

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.