/sci/ - Science & Math

>>15603115
>>15603281
Complex numbers have many applications in circuit analysis and, in general, frequency domain analysis. For example, the reactance of a capacitor or inductor is an imaginary number, and in general impedance is complex. But why? Because complex numbers, behaving as phasors, account for both magnitude and phase shift. You cannot use a real number to account for any phase shift other than 180 degrees. Complex numbers must be used in order to account for phase shifts other than 180 degrees. The reason complex numbers are used instead of “regular” 2 dimensional vectors, is that complex numbers have a very convenient definition of multiplication and division.