Question

What is the value of i^20+1?

everyone on here is saying that it’s 2 ? but my options are:

A. 1
B. -1
C. -i
D. i

Answer 1

You know

`i^2=-1`

Squaring both sides gives

`(i^2)^2=(-1)^2\implies i^4=1`

Then raising both sides to any integer power
`n` gives

`(i^4)^n=1^n\implies i^(4n)=1`

That is, any power of
`i` where the power is a multiple of 4 will always be equal to 1.

So

`i^(20)+1=1+1=2`

But perhaps you mean to write 20+1 as the exponent, in which case

`i^(20+1)=i^(20)i=i`