Question

Explain, in complete sentences, the pattern of exponents on the imaginary number i. What is the usefulness of knowing this pattern when performing operations on complex numbers?

Answer 1

the pattern is modular, or clock, arithmetic. there are only 4 states that it can take regardless of what the exponent is

Answer 2

i^0 = 1
i^1 = i
i^2 = -1
i^3 = -i

Answer 3

divide the exponent by 4; and see what your remander is to determine its equivalent value

Answer 4

and let me add that by "remainder" amistre means whole number remainder. like when you divide 103 by 4 the remainder is 3

i have noticed some confusion on this point