If R is not 50 ohm

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In general, the feed point impedance of an antenna is Z=R+jX, where R could be either greater than or less than 50 ohm.

First, let’s think of a case, for example, in which Z=100+jX. Now Z can be anywhere on the r=2 circle (blue on the right) and it is obvious that Z is most close to the origin (red dot) when X=0.

This can also be confirmed by looking at the two blue circles which are mutually tangent to each other, the point of the contact being at X=0.

The same can be said for any R > 50, which you can see immediately from the figure if you imagine two such blue circles.

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