Whats the procedure to determine the argument of this? (1 Viewer)

[Run hard@thehsc]

 

[cossine]

View attachment 35208

So finding the locus is based on the exterior angles of a triangle (Read some MM2 textbook).

If memory serves well straight line joining the dots is the 180 degrees.

So you have

arg([z-i]/[z-1]) = 180

 

[Run hard@thehsc]

@cossine how do you know which point goes on the top and which on the bottom when you write it out in that argument form?

 

[cossine]

@cossine how do you know which point goes on the top and which on the bottom when you write it out in that argument form?

You will go anticlockwise from the numerator to the denominator when you have positive angle. When you have an negative angle you will go clockwise from the numerator from the denominator.

In this particular case I don't think it will matter. As if you go anticlockwise from the numerator to the denominator or anticlockwise from the denominator to the numerator you will get the same result.