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

Question

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

+4​

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Quinn 3 weeks 2021-08-19T22:43:33+00:00 2 Answers 0 views 0

Answers ( )

    0
    2021-08-19T22:44:50+00:00

    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)2−4×2=x4+4×2+4−4×2=x4+4

    pleAse thanks bhi kar diya karo

    0
    2021-08-19T22:45:03+00:00

    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+4×2+4-4×2

    =x4+4

    Regards

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