Question

Find the equation in Cartesian coordinates of the locus of z if. |z-3| = 2​

Answer 1

Answer:

$(x-3)^{2}+y^{2}=4$

Step-by-step explanation:

Let us assume that z= x+iy.

Hence, in the Cartesian coordinates system point z is located by the coordinates (x,y).

Now, given that, |z-3| = 2​, ⇒ |(x-3)+iy| = 2​.

⇒$\sqrt{(x-3)^{2}+y^{2}  }=2$

⇒$(x-3)^{2}+y^{2}=4$.

So, this is the locus of z in Cartesian Coordinates, which nothing but an equation of a circle with center at (3,0) and radius 2 units.

(Answer)