SOLUTION: Looking to write a quadratic equation in the form ax^2+bx+c=0 , having roots of 1+i and 1-i. Not good with the "i" usage. Does below look correct? For X1 I foiled (1+i)(1-i) to

Algebra ->  Graphs -> SOLUTION: Looking to write a quadratic equation in the form ax^2+bx+c=0 , having roots of 1+i and 1-i. Not good with the "i" usage. Does below look correct? For X1 I foiled (1+i)(1-i) to       Log On


   

Question 744171: Looking to write a quadratic equation in the form ax^2+bx+c=0 , having roots of 1+i and 1-i. Not good with the "i" usage. Does below look correct?
For X1 I foiled (1+i)(1-i) to get -1
X2 would be it's conjugate, 1
Using quadratic equation (x-x1)(x-x2) I came up with x^2+0x-1=0
Thanks for your help!
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
USING YOUR STRATEGY:
A simple equation with 1%2Bi and 1-i for roots is
%28x-%281%2Bi%29%29%28x-%281-i%29%29=0 --> %28x-1-i%29%28x-1%2Bi%29=0 --> %28x-1%29%5E2-i%5E2=0 --> %28x-1%29%5E2%2B1=0 --> x%5E2-2x%2B1%2B1=0 --> highlight%28x%5E2-2x%2B2=0%29

ANOTHER APPROACH:
x = 1 ± i --> x-1 = ± i --> %28x-1%29%5E2=i%5E2 --> x%5E2-2x%2B1=-1 --> x%5E2-2x%2B1%2B1=0 --> highlight%28x%5E2-2x%2B2=0%29