Helicopter needs a tail rotor and the blades of the main rotor have to be articulated – they have to change pitch as the blade goes around the circle to allow the helicopter to hover or fly forward or to sides. This mechanism is very complicated and very expensive.
With quadcopter you need four rotors with fixed pitch – basically normal propellers run by four motors. You then simply control the rotation of individual motors through electronics. MUCH simpler construction.
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