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 in multiple of 4. So you can divide the exponent of i and the remainder tells you whether your answer is in terms of i, -1, -i, or 1.

Answer 2

\[i^1=i\]\[i^2=-1\]\[i^3=-i\]\[i^4=1\] and the pattern repeats ...\[i^5=i\]