Copy of Multiplying Complex Numbers

Describe the process of multiplying two complex numbers.

The number 1 is the multiplicative identity, because any number n times 1 equals n. What would the multiplicative identity be in the complex numbers (in a+bi form)?

Set a and c equal to 2, set b equal to -3, and set d equal to 3. What is the product? What if you change b to 1 and d to -1? When two complex numbers have the same a value but opposite b values, they are called complex conjugates (or sometimes just "conjugates"). Try another set of complex conjugates. What do all of their products have in common? Why does that happen?

Let a=4 and b=0. Let c=0 and d=1. What is the product? Set a and b so that z₁ is the same number as your product just was. Leave c and d the same. What is the new product? Do this two more times and record the product each time. Where did you end up?