Convert the rectangular form of the complex number 2-2i into polar form. Show all work and label the modulus and argument.
To convert the complex number 2-2i into polar form, we first need to find the modulus and argument.
Given complex number: z = 2 - 2i
Modulus (r):
r = |z| = √((2)^2 + (-2)^2) = √(4 + 4) = √8 = 2√2
Argument (θ):
θ = arctan(-2/2) = arctan(-1) = -π/4
Therefore, the polar form of the complex number 2-2i is:
z = 2√2 * cis(-π/4)