Question

Show that 1+i^10+i^20+i^30 is a real no.

Answer 1

i¹⁰=-1

i²⁰=1

i³⁰=-1

1+(-1)+1+(-1)=0

0 is a real number,

So, we can say that the value of 1+i¹⁰+i²⁰+i³⁰ is a real number.