Question

Prove that: (x+1+i) (x+1-i) (x-1+i) (x-1-i)= x4

+4​

Answer 1

Answer:

(x+1+i)(x+1−i)(x−1+i)(x−1−i)

= [(x+1)2−i2][(x−1)2−i2]

= (x2 +2x+1+1)(x2−2x+1+1)

= [(x2 +2)+2x][(x2+2)−2x]

= (x2+2)2−4x2=x4+4x2+4−4x2=x4+4

pleAse thanks bhi kar diya karo

Answer 2

Step-by-step explanation:

Taking RHS,

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

= [(x+1+i) (x+1-i)][ (x-1+i) (x-1-i)]

=[(x+1)2-i2][(x-1)2-i2]

=[x2+1+2x+1][x2-2x+1+1]

=[(x2+2)+2x][(x2+2)-2x]

=x4+4x2+4-4x2

=x4+4

Regards