Euler's formula is essential for converting between the time domain and the phasor domain, simplifying complex number multiplication in polar format. Using phasors makes solving AC circuit problems more efficient compared to traditional methods like differential equations. While it's possible to solve these circuits without Euler's formula, utilizing it streamlines the process significantly. The polar notation enhances clarity and ease of calculations in circuit analysis. Ultimately, Euler's formula is a valuable tool for engineers dealing with phasors in electrical circuits.