Finding original algebraic equation

[-EquinoX-]

Homework Statement

if I have a root of a +/- bi

i = imaginary number

what should the original algebra eqution?

Homework Equations

The Attempt at a Solution

 

[Mark44]

The original polynomial should have factors of (x - (a + bi))(x - (a - bi)), or equivalently, a single factor of (x² - 2ax + a² + b²). If the degree of the polynomial you're working with is larger than 2, there will be other roots, as well.

 

[HallsofIvy]

x- (a+ bi) and x- (a- bi) are factors. Multiply (x- (a+bi))(x- (a- bi)= ((x-a)- bi)((x-a)+bi)= (x-a)^2+ b^2 and set it equal to 0.

 

[-EquinoX-]

thanks Mark, shouldn't it be a^2 - b^2?

 

[Mark44]

thanks Mark, shouldn't it be a^2 - b^2?

Nope. The a² + b² comes from multiplying (-(a + bi))(-(a - bi)) = (a + bi)(a - bi) = a² -b²i² = a² + b².