Question

the value of (1+i)⁴ + (1-i)⁴ is ______?​

Answer 1

Correct option is

C

−8

(1+i)

4

+(1−i)

4

⇒ [(1+i)

2

]

2

+[(1−i)

2

]

2

We know, (a+b)

2

=a

2

+2ab+b

2

and (a−b)

2

=

2

−2ab+b

2

⇒ [1+2i+i

2

]

2

+[1−2i+i

2

]

2

⇒ [1+2i−1]

2

+[1−2i−1]

2

[ i

2

=−1 ]

⇒ (2i)

2

+(−2i)

2

⇒ 4i

2

+4i

2

⇒ −4−4

⇒ −8

∴ (1+i)

4

+(1−i)

4

=−8

Answer:

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