How to Sketch a Locus on the Argand Diagram for a Complex Equation?

[dave1987]

given z is complex, sketch the following locus on the Argand diagram:

{(z-3+j)/(z-j) }= square roots of 5

{ }= modulus .

hope anyone can guide .

 

[HallsofIvy]

First, you use "i" instead of "j" like a normal human being, not an engineer!

"Square" both sides to get
[tex]\frac{(z-3+ i)(\overline{z}-3-i)}{(z+i)(\overline{z}- i)}= 5[/itex]<br /> Setting z= x+ iy that is<br /> [tex](x-2 + i(y+1))(x- 2)- i(y-1)= 5(x+ i(y+1))(x- i(y-1))[/itex]<br /> <br /> Multiply that out and separate real and imaginary terms.[/tex][/tex]