Answer: -1
================================================
Work Shown:
Recall that the imaginary number i has the definition of
List out the first few powers of i
- i^0 = 1
- i^1 = i
- i^2 = -1
- i^3 = -i
- i^4 = 1
I'm skipping steps when I listed out those terms, so let me know if you need to see them.
The process repeats every 4 items. This means we'll divide the exponent by 4 to look at the remainder.
Let's do that for the first exponent
12/4 = 3 remainder 0
The remainder 0 tells us that i^12 = i^0 = 1
Also,
22/4 = 5 remainder 2
The remainder 2 means i^22 = i^2 = -1
-------------------
In short: i^12 = 1 and i^22 = -1
which means 6i^12 + 7i^22 = 6(1) + 7(-1) = -1