If $$|z-(3+4\iota)|\le 3$$ find the complex number with least magnitude satisfying the above inequality.
I recognized that the inequality represents the interior and circumference of a circle set in the Argand Plane with radius 3, centered at $(3,4)$. This is unfortunately as far as I got with the problem. $$$$ A friend of mine mentioned that z of the least magnitude is where the line joining the Origin to the center of the circle meets the circle's circumference. This seemed a very arbitrary declaration to me for I couldn't understand why this is so. I've tried to prove this proposition, but have so far been unable to. $$$$ I would greatly appreciate any help with this problem. While all methods are welcome, a method using the Rotation Theorem is preferred as this problem was initially part of a series of practice problems on the Rotation Theorem.