Question:
For a positive integer n, find the value of (1 – i)n
(1 – 1/i)n.
Solution:
According to the question,
We have,
$(1-i)^{n}\left(1-\frac{1}{i}\right)^{n}=(1-i)^{n}\left(1-\frac{1}{i^{2}}\right)^{n}$
= (1 – i)n (1 + i)n
= (1 – i2)n
= 2n
Therefore, (1 – i)n (1 – 1/i)n = 2n