Explain how to do this? i^6= a. -1 b. 1 c. -i d. i

Ok, so "i" was invented to allow algebra math problems to continue, despite containing the square root of a negative. The square root of a negative can't be solved because anything squared will become positive.
In other words, square root of -25 is not solvable because -x * -x = +x^2
To make solving manageable, mathematicians created the square root of negative one (-1) as this imaginary entity (i).
Let's use that square root of -25 again:


So in plain terms, it's as simple as this:

without doing too many examples, I want you to understand this pattern:
whenever the exponent of i is EVEN, then the answer will not have a radical !!
Why? because every couplet of i's will = i^2 which = -1
BUT an ODD numbered exponent of i will always leave that extra i after all the couplets become -1.

It's a little complicated in that every couplet will become -1, but if you have pairs (2) of COUPLETS, then -1×-1 = 1
So a couplet (2) × a pair (2) of couplets = 2×2=4
That means that if the even exponent is divisible by 4 (4, 8, 12, 16, etc.), then the answer will ALWAYS be +1. Otherwise the even exponent 2, 6, 10, 14, etc.) will result in a -1.

Now for our actual problem!!

Proof: