Minimum value of |z| for the locus of a complex number z

algebra-precalculuscomplex numbers

I have a question that involves an Argand diagram. The complex number u = 1 + 1i is the center of that circle, and the radius is one. In other words, $$|z – (1 + 1i)| = 1$$

Now my issue is the following: I need to calculate the least value of |z| for the points on this locus using the diagram. Here's the sketch:

enter image description here

So how do I find that least |z|? I understand that it'll involve a tangent to the circle, and I assume it's on the bottom right side of the circle, closest to the origin, but I'm not sure how to go about doing this.

Best Answer

Hint: Join a line from the origin to the center of the circle, once that is done ... label each term geometrically.

Note: $|z|$ is distance of the point $ z$ from the origin

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