How do you factor x^2+1?

1 Answer
Gió
May 5, 2015

You can do it using Complex Numbers! A complex number is given as a+ib where i=sqrt(-1) represents the Immaginary Unit (notice that sqrt(-1) cannot be evaluated as a real number so you call it simply i).
In your case you have that, to get x^2+1, you need to use two complex numbers:
(x+i)(x-i)
Try to multiply them remembering that i=sqrt(-1)
You get:
x^2-ix+ix-i^2=
but i^2=[sqrt(-1)]^2=-1 so
=x^2cancel(-ix)+cancel(ix)-i^2=x^2+1

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