Question

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

Answer 1

Answer: x = 1 + 2i, x = 1 - 2i

Explanation:

As we start solving this equation, we see that we have a square root of a negative number. There are no real solutions to this equation, only negative ones.

Given:

(x - 1)² = -4

Square root both sides of the equation:

x - 1 = ±
`√(-4)`

The square root of -4:

➜
`√(-1)` = i

x - 1 = ± 2i

Add 1 to both sides of the equation:

x = 1 ± 2i