For each , prove:

Okay.. so I need help with this. I thought the best way to prove these is by induction? So is induction something like:

Basis step, let k = 1.

i^{4*1} = i^{4} = 1 and hence it works

Now assume its true for . Prove that it's true for

We know that i^{4k} is 1, and i^{4} is 1, and hence it's true?

Something along those lines?