The imaginary number i is defined such that i2 = –1. What does i + i2 + i3 + ... + i23 equal?

Answer 1

did you mean
i + i^2 + ... + i^23 ?

notice this pattern

i^1 = i
i^2 = -1
i^3 = -i
i^4 = +1
i^5 = i
....

notice that
i + i^2 + i^3 + i^4 = 0 and
i^5 + i^6 + i^7 + i^8 = 0
etc

let me know what you got.