Directions: Using the integers -9 to 9 at most one time each, fill in the boxes twice: once to make a positive real number product and once to make a negative real number product. You may reuse all the integers for each product.

### Hint

What is the difference between a real and complex number? What causes an i to go away during multiplication? What causes a term to go away during binomial multiplication? How do we choose integers such that the i terms are additive inverses of one another? Once we find one real number product, how might we find one of the opposite sign?

### Answer

There are many answers, but one is (3 + 6i)(2 + -4i) for the positive solution and (-3 + -6i)(2 + -4i) for the negative solution.

Source: Robert Kaplinsky in Open Middle Math