Math Help??

Question

Suppose that your friend describes a method of simplifying a positive power I. “Just divide the exponent by 4, and then look at the remainder. Then. Refer to the short table of powers of I in this section. The given power of I is equal to I to the power indicated by the remainder, And if the remainder is 0, the result is i^0=1” Explain why this method works.

Answer 1

I^0 by definition is 1 as is true of any zero exponent

I^1=I because any quantity raised to the first power is itself

I^2=-1 stems from the definition of I being the square root of -1

I^3 = I^2*I^1 = -1I

I^4 = (I^2)^2 = (-1)^2 = 1

I^5 = I^4 * I^1 = 1*I = I = I^1

I^6 = I^5 * I^1 = I*I = I^2 = -1

 

You can already start to see the pattern forming with cycle 4