Now, let’s think of a case, for example, in which Z=10+jX.
This time Z can be anywhere on the r=0.2 circle (outer brown circle) and you can see from the figure that Z is again most close to the origin (red dot) when X=0.
See that the two brown circles (outer and inner ones) are mutually tangent to each other, the point of the contact being at X=0.