Electricity and electrical components occupy an important place in our lives today. Our lives come to a virtual halt when the power goes out or our electrical appliances stop working. Sometimes we even start to panic because we are so dependent on these components that we cannot afford to lose them. Their importance and use only increases as we lose them. time passes. We all use these electrical devices as well as electricity itself, but most of us don't think about the math and physics behind all these things. In this article, I will talk about how AC circuits can be described by considering voltage and current using complex numbers. An AC circuit requires two distinct numbers to fully describe it. Indeed, it takes into account the amplitude and phase of the current. The fact that complex numbers can be easily added, subtracted, multiplied or divided with each other makes them ideal for this operation where amplitude and phase must work together. For a DC circuit, Ohm's law is used. According to Ohm's law, v=iR Where, v= voltage i= current flowing in the circuitR= resistance offered by the resistors fixed in the circuit. Whereas there is an AC analogy for the Ohms that are used. Here, the equation of Ohm's law becomes: v=iZ Where, v= voltage i= current flowing in the circuitZ= impedanceHere, all three quantities can be used as complex numbers. Z defines a quantity called impedance. Impedance acts in the same way as resistance in a DC circuit. Moreover, if the frequency of the AC circuit can reach 0, the impedance will go down to 0 because the imaginary part of it will disappear, thus making it equal to the resistance of a DC circuit. In the article, the following...... middle of paper ......the original vector.P*=A-jBThe modulus of a complex number is the square root of the sum of the squares of each real and imaginary part of the number. It is denoted |P| if P is the complex number.|P|=√(A^2+B^2)A complex number can also be expressed in polar form using Euler's formula:P=A+jB=exp⁡(jθ) =cosθ +jsinθAlso,P=|P|exp⁡(jθ)And tanθ=B/A Relationship between AC circuit and complex numbers Complex numbers provide a structure for describing sinusoidal functions of time, especially current functions and voltage observed in AC circuits. .The exponential of complex numbers is the most useful because the relationship between voltage and current is close to multiples. In sinusoidal voltages, different types of impedances/resistances exist. Here I'm talking specifically about capacitors and inductors, excluding non-linear devices.