Simplifying Complex Quadratic Equations

[duki]

Homework Statement

x^2 + (1-i)x + (-6 + 2i) = 0, solve in terms of a + bi

Homework Equations

The Attempt at a Solution

Here's what I have so far... But I could be wrong.

x = -(x-xi) +/- sqrt[ (x-xi)^2 - 4(-6 + 2i) ] / 2

x = -(x-xi) +/- sqrt[ (x^2 - 2xi + xi^2) + 24 - 8i ] / 2

I'm having trouble simplifying this part. Did I do something wrong?

 

[eok20]

Remember that x should not be on the right hand side of the equation; b is just 1-i, not (1-i)*x.

 

[duki]

Ohhhh snap. Let me try again.

 

[duki]

So now I get to

-(1 - i) +/- sqrt[ 25 - 10i + i^2 ] / 2

And again, I'm stuck on the simplification.

 

[djeitnstine]

Check for factors, you have another quadratic under the root

 

[duki]

So I factor that to (i - 5)^2 and get:

-(1 - i) +/- (i -5) / 2...