Explanation
(1 + i)^10 can be expanded using the binomial theorem:
(1 + i)^10 = 1 + 10i + 45i^2 + 120i^3 + ... + 10i^9 + i^10
Since i^2 = -1, i^3 = -i, i^4 = 1, and so on, we can simplify the expression:
(1 + i)^10 = 1 + 10i - 45 - 120i + ... - 10i + 1
= 2 - 130i
= -128 + 128i
= 128(-1 + i)
= 32(4(-1 + i))
= 32(-4 + 4i)
= 32(-4(1 - i))
= 32(4(i - 1))
= 32(-1)(4(i - 1))
= 32i
So, (1 + i)^10 = 32i.