SOLUTION: What is th value of 1+i+i^2+i^3+i^4+i^5+i^6+i^7+i^8+i^9+i^10+i^11+i^12+i^13+i^14+i^15+i^16+i^17+i^18+i^19+i^20

Algebra ->  Complex Numbers Imaginary Numbers Solvers and Lesson -> SOLUTION: What is th value of 1+i+i^2+i^3+i^4+i^5+i^6+i^7+i^8+i^9+i^10+i^11+i^12+i^13+i^14+i^15+i^16+i^17+i^18+i^19+i^20      Log On


   

Question 301620: What is th value of
1+i+i^2+i^3+i^4+i^5+i^6+i^7+i^8+i^9+i^10+i^11+i^12+i^13+i^14+i^15+i^16+i^17+i^18+i^19+i^20
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
First calculate your terms
i%5E1=i
i%5E2=-1
i%5E3=-i
i%5E4=1
.
.
i%5E5=i
i%5E6=-1
i%5E7=-i
i%5E8=1
You see the recurring pattern.
The sum from i%5E1 to i%5E4 =i-1-i%2B1=0
Similarly
The sum from i%5E5 to i%5E8 =i-1-i%2B1=0
The sum from i%5E9 to i%5E12 =i-1-i%2B1=0
The sum from i%5E13 to i%5E16 =i-1-i%2B1=0
The sum from i%5E17 to i%5E20 =i-1-i%2B1=0
So then,