Question

Show that 1+i^10+i^100-i^1000=0​

Answer 1

Step-by-step explanation:

$1 + i^10 \: + i^100 \: - i^1000 \\ 1 + (i^{2})^5 \: \: + (i^{2})^50 - (i ^{2})^500 \\ 1 + ( - 1)^5 + ( - 1)^50 \: - ( - 1)^500 \\ 1 - 1 + 1 - 1 = 0$