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Exploring the Argand diagram

and are complex numbers. is the product Move the points and around to see what happens to
Fix , and move until is on the x-axis. What can you say about the trajectory of as you move it to keep on the x-axis? Repeat the above for other values of : Can you make predictions about where needs to be for to be on the x-axis? Can you predict where needs to be when you want 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 on the y-axis.