Can you figure out two complex numbers where neither a nor b are zero that when multiplied together become a real number?

Answer 1

This might be a complex number and its conjugate: (a + bi) times (a - bi). More generally, any two complex numbers such that the angle formed by one is the negative of the angle formed by the other. In other words, you can multiply the conjugate by any real constant and still get a real result: (a + bi) times (ca - cbi).

Specific examples:

Multiply (3 + 2i) times (3 - 2i).

Multiply (3 + 2i) times (6 - 4i).

Answer 2

Any complex number multiplied by it's conjugate will do, i.e., (a + bi) (a - bi)