How can I write (1+i)^101 in its simplest form? The answer is: 2^50(1+i), but I do not know how to get to that.

Answer 1

1+i = √2 cis π/4

(1+i)^101 = (√2)^101 cis (π/4 * 101)
= 2^50 √2 cis (25π + π/4)
= 2^50 √2 cis 5π/4
= 2^50 (-1-i)
or -2^50 (1+i)

There appears to be a typo.