Note: Enter your answer and show all the steps that you use to solve this problem in the space provided. 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 from rectangular form to polar form, we first need to find the modulus and argument.
The modulus (r) can be found using the formula:
r = √(a^2 + b^2)
For the complex number 2 - 2i, a = 2 and b = -2:
r = √(2^2 + (-2)^2)
r = √(4 + 4)
r = √8
r = 2√2
The argument (θ) can be found using the formula:
θ = arctan(b/a)
For the complex number 2 - 2i, a = 2 and b = -2:
θ = arctan(-2/2)
θ = arctan(-1)
θ = -π/4
Therefore, the polar form of the complex number 2 - 2i is:
2√2 * cis(-π/4)