Consider the differential equation of an RLC circuit. In analogy with the damped harmonic oscillator, the solution of the RLC circuit equation is given by an exponential function. Differentiating the solution twice with time and substituting the resistance factor and oscillation frequency gives a quadratic equation with two possible solutions. The sum of these gives the final solution to the RLC circuit equation. Consider the underdamped case, where the resistance factor is less than the oscillation frequency. In this case, the solution becomes imaginary. On substituting the imaginary term, the complex solution of the underdamped RLC circuit is obtained. By using Euler's formula, the equation is simplified. For the equation to be real, A1 and A2 have to be complex conjugates of each other, which further simplifies the solution. Expressing the coefficients in terms of charge amplitude and substituting the resistance factor, the final solution for the underdamped RLC oscillator is obtained. Here, ω' and Φ represent the angular frequency and the phase angle of the underdamped RLC circuit, respectively.