Question

Prove that (x +1+i) (x +1-i) (x - 1+i) (x - 1 - i) = x⁴ + 4​

Answer 1

Step-by-step explanation:

(x+1+i)(x+1-i) (x-1+i)(x-1-i)

[(x+1)^2+1] [(x-1)^2+1]

(x2 + 1 + 2x + 1) (x2 + 1 -2x + 1)

(x2 + 2 + 2x) (x2 + 2 - 2x)

[(x2+2)^2 - 4x^2]

x^4 + 4 + 4x^2 - 4x^2

x^4 + 4

hence proved