Question

Find the value of (1-i)8

Answer 1

Given,

$(1-i)^8$

We have to find the value of $(1-i)^8$ =?

Solution:

∴ $(1-i)^8$

= $((1-i)^2]^4$   [∵ $(a^m)^n=a^{mn}$ ]

= $(1+i^2-2i)^4$

= $(1-1-2i)^4$ [ ∵ $i^2$ = - 1]

= $(-2i)^4$

= 16 × $(i^{2})^2$

= 16 × $(-1)^2$  [ ∵ $i^2$ = - 1]

= 16 × 1

= 16

∴ $(1-i)^8$ = 16

Thus, the value of $(1-i)^8$ is "equal to 16".