How do you solve (x-2)^2=-3?

1 Answer
George C.
May 1, 2016

x = 2+-sqrt(3)i

Explanation:

To solve this we want to take the square root of both sides, but the right hand side is negative. If a is any Real number then a^2 >= 0, so we need a Complex number, in this case sqrt(3)i.

If a < 0 then sqrt(a) = sqrt(-a)i

So given:

(x-2)^2 = -3 = (sqrt(3)i)^2

We must have:

x-2 = +-sqrt(3)i

Note the +-, since if a^2 = b then (-a)^2 = b too.

Then adding 2 to both sides we get:

x = 2+-sqrt(3)i

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