Argand diagram (locus)

[ForeignHorse]

When I substitute z=x+yi, I can't seem to work out the answer. Anyone knows how to solve this ? Thanks

[studiot]

The equation says

 

The modulus of the expression = 1.

 

The modulus is a real number, what is the expression for it in terms of x and y?

What is the locus of all point in the x - y plane whose modulus is 1?

 

 

 

You should be able to plot expressions ax+by = 1 on the xy plane; What does that plot look like?

 

 

 

Let the complex quotient in the expression be equal to [math]\alpha x + \beta iy[/math]

 

Then reduce the quotient to this form and equate coefficients; Do you know how to reduce a complex quotient to a single complex number (ie bring the complex part from the bottom to the top) ?

Edited February 22, 2015 by studiot