Question

(1+i)^4 +(1-i)^4 =?
a)8
b)4
c)-8
d)-4​

Answer 1

Answer:

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Answer 2

Answer:

(1+i)^4 +(1-i)^4

$= {(1 + {i}^{2} + 2i)}^{2} + {(1 + {i}^{2} - 2i )}^{2}$

$= 1 + {i}^{4} + 4 {i}^{2} + 2 {i}^{2} + 4 {i}^{3} + 4i \: \\ + 1 + {i}^{4} + 4 {i}^{2} + 2 {i}^{2} - 4 {i}^{3} - 4i$

$= 1 + {i}^{4} + 4 {i}^{2} + 2 {i}^{2} \\ + 1 + {i}^{4} + 4 {i}^{2} + 2 {i}^{2}$

$= 2 + 2{i}^{4} + 12{i}^{2}$

$= 2 + 2 - 12 \\ = 4 - 12 \\ = - 8$