\(x^2 -2x + 3 - 2i\sqrt{3} =0\)

Hello! How would I go about solving this particular equation? Factoring this seemed awful, I tried factoring out sqrt(3) out of 3 and 2i*sqrt(3) but ended up with nothing useful since the i is still there. Using the quadratic formula gave me a complex number in the root sign and I'm not sure how to handle that. What about if the x^2 had a i attached to it? So this one for instance:

\(ix^2 -2x + 3 - 2i\sqrt{3} =0\)

Thanks!

Quazars
Oct 12, 2017

#1**+1 **

x^2 + 2x + 3 -2i√3 = 0 rearrange as

x^2 + 2x = -3 + 2i√3

Take 1/2 the coefficient on x = 1......square it = 1 and add to both sides

x^2 + 2x + 1 = -3 + 2i√3 + 1 factor the left side....simplify the right side

( x + 1)^2 = -2 + 2i√3 factor the right side

(x + 1)^2 = 2 (i√3 - 1) take both roots

x + 1 = ±√ [ 2 (i√3 - 1) ] subtract 1 from both sides

x = ±√ [ 2 (i√3 - 1) ] - 1

CPhill
Oct 12, 2017