Write z=9-3 squareroot 3 i in polar form. (1 point)
To convert the complex number z = 9 - 3√3i to polar form, we first need to find the modulus (r) and the argument (θ) of the complex number.
Given that z = 9 - 3√3i, we can find r as:
r = √(9^2 + (-3√3)^2)
r = √(81 + 27)
r = √108
r = 6√3
Next, we can find the argument θ using:
θ = arctan(Imaginary part / Real part)
θ = arctan((-3√3) / 9)
θ = arctan(-√3/3)
θ = -π/3
Therefore, z = 9 - 3√3i in polar form is:
z = 6√3 cis(-π/3)