### 3 Answers

Relevance

- L. E. GantLv 71 month ago
Find 1234567890 mod 4...

then look at the pattern

i^1 = sqrt(-1)

i^2 = -1

i^3 = i^2 * i = -1*i = -i

i^4 = i^2 * i^2 = (-1) * (-1)

so 1234567890 mod4 = 2

hence i^1234567890 = i^2 = -i

- llafferLv 71 month ago
"i" is an imaginary number that loops every 4 times through:

i⁰ = 1

i¹ = i

i² = -1

i³ = -i

So if the exponent is a multiple of 4, then the result is 1. Whatever the remainder is after dividing by 4 will tell us which of the other 3 possible options it is.

So divide and check the remainder:

1234567890 / 4 = 308641972 R 2

Since the remainder is 2, your expression simplifies to:

-1

Still have questions? Get answers by asking now.