Question

Find all the values of log(3-2i)

Answer 1

I will assume you want:
ln(3-2i)
I will assume that you are familiar with De Moivre's Theorem
and the definition for r e^(θi)

let z = ln(3-2i)
then e^z = 3-2i
= √13 e^(5.695i) <---- from r^2 = 3^2 + (-2)^2 and tanθ = -2/3 in quadrant IV
= (e^(ln √13) * e^(5.695i) <----- log property: e^(ln k) = k
= e^( ln √13 + 5.695i)

so if e^z = e^( ln √13 + 5.695i)

z = ln √13 + 5.695i