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A λ/4 antenna with a groundplane has an impedance which is mostly resistive rarther than reactive, is around 50-75ohms which is easy to match to transmitters and has a radiation pattern that is reasonably suited to typical uses of radio equipment such a a two way radio in a car where you want the tranmitted energy to go out perpendicular to the antenna rarther than up into the sky and uselessly out into space.
First of all not always the monopole is a quarter-wave. Could be λ/8 (the peak current located at a position well above the top, to give lower-angle of radiation and additional gain). Or if is a bent monopole could have different electrical length.
The impedance of a quarter-wave monopole (Marconi Antenna) with perfect ground, is 36.6 ohms.