SOLUTION: If {{{i=sqrt(-1)}}} Prove: {{{(x+1+i)(x+1-i)(x-1+i)(x-1-i)=x^2+4}}}

Algebra ->  Complex Numbers Imaginary Numbers Solvers and Lesson -> SOLUTION: If {{{i=sqrt(-1)}}} Prove: {{{(x+1+i)(x+1-i)(x-1+i)(x-1-i)=x^2+4}}}      Log On


   

Question 876195: If i=sqrt%28-1%29
Prove:
%28x%2B1%2Bi%29%28x%2B1-i%29%28x-1%2Bi%29%28x-1-i%29=x%5E2%2B4
Answer by josgarithmetic(39616) About Me  (Show Source):
You can put this solution on YOUR website!
Recognize how to associate terms in each trinomial factor to make use of difference of squares results.

%28%28x%2B1%29%2Bi%29%28%28x%2B1%29-i%29%28%28x-1%29%2Bi%29%28%28x-1%29-i%29=x%5E2%2B4
%28%28x%2B1%29%5E2-i%5E2%29%28%28x-1%29%5E2-i%5E2%29
Now keep going.