Question

Find the value of 1 + i^10+ i^20 + i^30​

Answer 1

Step-by-step explanation:

1+i¹⁰+i²⁰+i³⁰

1+(i²)⁵+(i²)¹⁰+(i²)¹⁵

1+(-1)⁵+(-1)¹⁰+(-1)¹⁵

1+(-1)+1+(-1)

1-1+1-1

0

Answer 2

Answer:

So, we can write it in the form of i(4×7+2). Hence we get the values of i10=−1,i20=1,i30=−1. We know that 0 is a real number. Therefore, it is proved that 1+i10+i20+i30 is a real number.

Step-by-step explanation:

So, we can write it in the form of i(4×7+2). Hence we get the values of i10=−1,i20=1,i30=−1. We know that 0 is a real number. Therefore, it is proved that 1+i10+i20+i30 is a real number.