Methods and apparatus for complex number generation and operation on a chip are disclosed. A disclosed logic device includes a first magnet with a first preferred direction of magnetization to polarize a spin of electrons in the first direction. The example logic device includes a second magnet with a second preferred direction of magnetization that polarizes a spin of electrons in the second direction. The example logic device includes a third magnet providing a free layer without a preferred direction of magnetization that is connected to the first and second magnets, wherein the third magnet encodes a vector based on a flux of electrons spin polarized in the first direction and a flux of electrons spin polarized in the second direction.