Three forms, one numberDefinition of complex numbersCartesian formAdditionMultiplicationExercise 1Complex conjugateAbsolute value or modulusDivisionPowers of iPolar formPolar coordinatesExercise 3Defining complex numbers in polar formExampleMultiplication and division in polar formExampleDe Moivre's theoremThe most beautiful equation in mathematicsExponential formExercise 4ConjugationMultiplicationExampleConjugate transpose of a matrixBloch sphereSummaryExercisesExercise 1Exercise 2Exercise 3Exercise 4References