Find all solutions to the equation equation (x - 1) ^2 = - 4.

x = 1±2i

Step-by-step explanation:

(x - 1) ^2 = - 4.

Take the square root of each side

sqrt ((x - 1) ^2) = sqrt (-4)

Sqrt (ab) = sqrt (a) sqrt (b)

We know the sqrt (4) = 2 and the sqrt (-1) = ±i

x-1 = ±2i

Add 1 to each side

x-1+1 = 1±2i

x = 1±2i