Complex numbers/roots of quadratics question

A) Find the square roots of -3 + 4i
I've done this part, I got 1 + 2i and -1 -2i.
B) Hence, or otherwise, find the two complex roots of the quadratic equation z^2 - 2(1+i)z + 3 - 2i=0

I'm somewhat suspicious of the first half of the question, so check the quadratic equation
z = { 2(1+i) +/- sqrt ( [-2(1+i)]^2 - 4(1)(3-2i) )} /2
z = { 2(1+i) +/- sqrt ( 4 + 8i -4 - 12+8i )} /2
z = { 2(1+i) +/- sqrt ( -12+16i )} /2
z = { 2(1+i) +/- sqrt ( 4(-3 +4i) )} /2 ..... see, I knew A would show up in question B
z = { 2(1+i) +/- 2*sqrt (-3 +4i) } /2
z = (1+i) +/- sqrt (-3 +4i)
z = (1+i) + 1 +2i = 2+3i (root 1)
z = (1+i) - 1 -2i = -i (root 2)

Which verifies when plugged back in. I hate complex equations.