Try an Example
Pick a scenario to see how the calculator works, then adjust the values
Signal Addition
Add two phasor signals in complex form to find the resultant.
Key values: z₁ = 3 + 4i · z₂ = 1 − 2i · Addition
Circuit Impedance
Divide two impedances to compute the transfer ratio.
Key values: z₁ = 3 + 4i · z₂ = 1 + 2i · Division
De Moivre Power
Raise a complex number to the 10th power using De Moivre's theorem.
Key values: z₁ = 1 + i · n = 10 · Power
Cube Roots of −8
Find all three cube roots of −8, visualized as equidistant points on a circle.
Key values: z₁ = −8 + 0i · n = 3 · nth Root
This calculator is also known as Phasor Calculator.
Read the complete guidePhasors in AC Circuit Analysis
In AC circuits, voltages and currents are sinusoidal. Phasors represent them as complex numbers: V = V_m∠θ. Impedance Z = R + jX combines resistance R and reactance X (inductive X > 0, capacitive X < 0). Series impedances add directly; parallel impedances use the reciprocal formula.
Examples
Series RLC Impedance
Add impedances Z₁ = 50 + j30 Ω and Z₂ = 20 − j10 Ω in series.
Z_total = (50+20) + j(30−10) = 70 + j20 Ω. |Z| = √(4900+400) ≈ 72.8 Ω, θ ≈ 15.95°.
Key takeaway: Series impedances add component-wise — resistances add and reactances add. The total impedance has a smaller phase angle than either individual.
AC Circuit Analysis Tips
Practical guidance for phasor calculations:
- Use rectangular form (R + jX) for series circuits where impedances add
- Use polar form (Z∠θ) for multiplication/division in transfer function calculations
- For parallel impedances, compute 1/(1/Z₁ + 1/Z₂) using complex division
Frequently Asked Questions about Phasor Calculator
Why do engineers use j instead of i?
In electrical engineering, i is reserved for current. To avoid ambiguity, the imaginary unit is written as j. Mathematically, j = i = √(−1).
What does the phase angle mean in a circuit?
The phase angle θ = arctan(X/R) indicates the phase difference between voltage and current. Positive θ means voltage leads current (inductive); negative means voltage lags (capacitive).
Specialized Calculators
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