Question:
The value of $(1+i)\left(1+i^{2}\right)\left(1+i^{3}\right)\left(1+i^{4}\right)$ is
(a) 2
(b) 0
(c) 1
(d) i
Solution:
(b) 0
$(1+i)\left(1+i^{2}\right)\left(1+i^{3}\right)\left(1+i^{4}\right)$
$=(1+i)(1-1)(1-i)(1+1) \quad\left(\because i^{2}=-1, i^{3}=-i\right.$ and $\left.i^{4}=1\right)$
= (1 + i) (0) (1
= 0