Final answer:
To simplify a power of i above 4, you divide the exponent by 4 and use the remainder to find the equivalent simple power of i (1, i, -1, or -i) as i's powers are cyclical every four.
Step-by-step explanation:
To simplify a power of i that is higher than 4, we divide by 4 to find the remainder. In complex numbers, i is the imaginary unit, where i squared equals -1. The powers of i are cyclical every four powers, that is, i to the power of 1 is i, to the power of 2 is -1, to the power of 3 is -i, and i to the power of 4 returns to 1.
Beyond i to the fourth power, the pattern repeats. Thus, when you have i to the power of any number higher than 4, you can simplify the expression by dividing the exponent by 4 and taking the remainder. The remainder will then tell you the equivalent simple power of i (1, i, -1, or -i).