[math]z_1[/math] and [math]z_2[/math] are complex numbers.[br][math]z_3[/math] is the product [math]z_1*z_2[/math][br]Move the points [math]z_1[/math] and [math]z_2[/math] around to see what happens to [math]z_3[/math]

Fix [math]z_1[/math], and move [math]z_2[/math] until [math]z_3[/math] is on the x-axis. What can you say about the trajectory of [math]z_2[/math] as you move it to keep [math]z_3[/math] on the x-axis?[br][br]Repeat the above for other values of [math]z_1[/math]:[br][br] Can you make predictions about where [math]z_2[/math] needs to be for [math]z_3[/math] to be on the x-axis?[br] Can you predict where [math]z_2[/math] needs to be when you want [math]z_3[/math] to be at a given point on the x-axis?[br][br][br]Can you use your understanding of multiplication of complex numbers to explain how to make these predictions? Take a look at [url=http://nrich.maths.org/9858]A Brief Introduction to Complex Numbers[/url] for a reminder of the notation and algebraic manipulation.[br][br]Now carry out the same process but this time aiming to keep [math]z_3[/math] on the y-axis.