1. Create different sets of expressions that satisfy each desired outcome:

a. Find a pair of complex binomials whose sum is 8 + 9i.

b. Find a pair of complex binomials whose difference is -2 + 6i.

2. Make a generalization about the exponents of imaginary numbers, regarding whether or not all even or all odd exponents result in real or imaginary numbers. Explain and prove your statement with actual examples and at least one complete sentence that supports your generalization.