$|2z+3|=|z+6|$ where $z$ is a complex number represents a circle with center $(0,0)$ and radius $3$. It is fairly easy to prove it by letting $z=x+iy$ and we get the standard equation of circle in cartesian form. But is there any way we can deduce $|z|=3$ without exploiting $z=x+iy$ e.g in cartesian form? The reason being the cartesian calculation is a tad bit tedious. So it will be helpful if someone suggests a clever way of manipulating this.