The complex number 3 - 3i can be written in the form a + bi, where a is the real part and b is the imaginary part. In this case, a = 3 and b = -3.
To convert a complex number from rectangular form (a + bi) to trigonometric form (r cis θ), we can use the following formulas:
r = |a + bi| = sqrt(a^2 + b^2)
θ = arctan(b/a) + kπ, where k is an integer and the angle is measured in radians.
In this case, we have:
r = sqrt(3^2 + (-3)^2) = sqrt(18) = 3sqrt(2)
θ = arctan((-3)/3) + kπ = -π/4 + kπ, where k is an integer.
To find the principal argument, we use k = 0:
θ = -π/4
Therefore, the complex number 3 - 3i in trigonometric form is:
3sqrt(2) cis (-π/4)
Converting this to degrees, we get:
3sqrt(2) cis (-45°)
So the answer is not one of the options given.