(z − 1)^2 + 4 = 0

Answer 1

(z-1)^2 = -4
z-1 = ±2i
z = 1±2i

Answer 2

if solving for z then you can foil out (z-1)^2 and add the constant to 4

you should have an equation in the form of ax^2+bx+c

Set the equation equal to 0 and solve for z. I would use the quadratic equation.
Your final answer with have imaginary numbers.