The value of
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  i) (2)

= 0

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