Complex Number to Phasor (Polar & Rectangular) Calculator
Convert complex numbers between Rectangular (a + bi) and Polar Phasor notation (r ∠ θ°), calculate impedance magnitude |Z|, phase angles, and AC power factor.
Calculated Results
Frequently Asked Questions
How do you convert complex rectangular numbers to polar phasor form?
Magnitude: r = sqrt(a^2 + b^2). Phase angle: theta = atan2(b, a). In AC circuit analysis, rectangular impedance Z = R + jX converts into polar phasor notation Z = |Z| ∠ theta.
What does the sign of the imaginary reactance (jX) indicate?
Positive imaginary reactance (+jX) represents inductive reactance (inductors, coils, motors), where current lags voltage. Negative imaginary reactance (-jX) represents capacitive reactance (capacitors), where current leads voltage.
What is the Power Factor (PF) in electrical engineering?
Power Factor is the cosine of the phase angle (PF = cos θ). A PF of 1.0 indicates a purely resistive circuit where all energy does real work. Inductive motors with low power factors (e.g. 0.70) draw excessive reactive current.
What is a complex conjugate and why is it used?
The complex conjugate of a + bj is a - bj. Multiplying a complex number by its conjugate eliminates all imaginary terms, yielding a purely real scalar (a^2 + b^2), which is essential for calculating apparent electrical power S = V × I*.