Simplifying Complex Quadratic Equations

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Homework Help Overview

The problem involves solving a complex quadratic equation of the form x^2 + (1-i)x + (-6 + 2i) = 0, with a focus on expressing the solutions in the form a + bi.

Discussion Character

  • Mixed

Approaches and Questions Raised

  • Participants discuss the initial setup of the quadratic equation and the application of the quadratic formula. There are attempts to simplify the expression under the square root, with some questioning the placement of variables and the simplification steps taken.

Discussion Status

Some participants have provided guidance on correcting the formulation of the equation, while others are exploring simplification techniques. There is an ongoing exploration of factoring and simplification, but no consensus has been reached on the final form of the solution.

Contextual Notes

Participants are navigating the complexities of working with complex numbers and quadratic equations, and there are indications of confusion regarding the manipulation of terms and the simplification process.

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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?
 
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Remember that x should not be on the right hand side of the equation; b is just 1-i, not (1-i)*x.
 
Ohhhh snap. Let me try again.
 
So now I get to

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

And again, I'm stuck on the simplification.
 
Check for factors, you have another quadratic under the root
 
So I factor that to (i - 5)^2 and get:

-(1 - i) +/- (i -5) / 2...
 

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