Imaginary numbers are the proof that even in mathematics you can discover stuff even though you don’t understand what you have found. Complex numbers encode rotation.
Yup. When you have a circuit that is not purely resistive the inductive or capacitive load causes the voltage and current to not be in phase. It looks like ohms law is being violated. However the missing part of the energy is in the imaginary component to be returned latter.
Ever since I went down a particularly nasty rabbit hole and came out with a tenuous grasp on quaternions, imaginary numbers started feeling very simple, familiar and logical.
Imaginary numbers are the proof that even in mathematics you can discover stuff even though you don’t understand what you have found. Complex numbers encode rotation.
Yup. When you have a circuit that is not purely resistive the inductive or capacitive load causes the voltage and current to not be in phase. It looks like ohms law is being violated. However the missing part of the energy is in the imaginary component to be returned latter.
Ever since I went down a particularly nasty rabbit hole and came out with a tenuous grasp on quaternions, imaginary numbers started feeling very simple, familiar and logical.