Math word problem

Question

I need some assistance with a question involving complex numbers. The question is:

Consider the complex number: 𝑧 = 3 − 3 𝑖. Evaluate:

(i) 𝐼𝑚(𝑧) (ii) |𝑧| (iii) 𝐴𝑟𝑔(𝑧)

Answer 1

(i) Im(z) = -3 (It is the number in front of i, with the sign included.)

(ii) |z| = √[3² + (-3)²] = ?

(iii) Arg(z) = arctan(-3/3) = ? (Be careful with the quadrant. Note this angle is in quadrant IV.)