Question

Value of (1+i)^4+ (1-i)^4 is
​

Answer 1

Step-by-step explanation:

We have,,

$\sf{(1+i)^{4}+(1-i)^{4}}$

$\sf{=[(1+i)^{2}]^{2}+[(1-i)^{2}]^{2}}$

$\sf{=[1+i^{2}+2i]^{2}+[1+i^{2}-2i]^{2}}$

Since, i² = -1

Therefore,

$\sf{=[1-1+2i]^{2}+[1-1-2i]^{2}}$

$\sf{=[2i]^{2}+[-2i]^{2}}$

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

$\sf{=8i^{2}}$

$\sf{=\boxed{\sf{-8}}}$

_____________________________________________

HOPE IT HELPS ❣️❣️❣️