How are phasors used to represent AC quantities and simplify calculations?

Phasors represent sinusoidal AC quantities as rotating vectors in the complex plane, with magnitude indicating peak or RMS value and angle indicating phase. They convert differential equations into algebraic equations by transforming time-domain sinusoids to frequency-domain complex numbers. Using phasors, AC circuit analysis becomes similar to DC analysis with complex impedances: V = IZ where all quantities are complex.