[math] and [math] are complex numbers.
[math] is the product [math]
Move the points [math] and [math] around to see what happens to [math]
Fix [math], and move [math] until [math] is on the x-axis. What can you say about the trajectory of [math] as you move it to keep [math] on the x-axis?
Repeat the above for other values of [math]:
Can you make predictions about where [math] needs to be for [math] to be on the x-axis?
Can you predict where [math] needs to be when you want [math] to be at a given point on the x-axis?
Can you use your understanding of multiplication of complex numbers to explain how to make these predictions? Take a look at A Brief Introduction to Complex Numbers for a reminder of the notation and algebraic manipulation.
Now carry out the same process but this time aiming to keep [math] on the y-axis.