Question

What is the value of (1+i)^4+(1-i)^4

Answer 1

Answer:

-8 is the answer..

Step by step solution:

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

=>[(1+i)^2]^2 + [(1-i)^2]^2

We know that, (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 is the answer..

I hope this answer is helpful for you...