🎯 Input Formats

Rectangular Form: Enter real and imaginary parts (a + jb)

Polar Form: Enter magnitude and angle in degrees (r∠θ°)

Example: 5 + j3 or 5.83∠30.96°

➕ Adding Phasors

Click "Add Phasor" to include more complex numbers in your calculation

The calculator supports up to 8 phasors simultaneously

Mix rectangular and polar formats as needed

📊 Results

Results are displayed in both rectangular and polar forms

Step-by-step solutions show conversion and addition process

Copy results to clipboard for use in other applications

💾 History

Last 10 calculations are automatically saved

Click on any history item to view details

History persists between browser sessions

🔢 Complex Numbers

A complex number has the form z = a + jb, where:

• a is the real part

• b is the imaginary part

• j is the imaginary unit (√-1)

📐 Polar Form

Polar form: z = r∠θ, where:

• r = √(a² + b²) (magnitude)

• θ = arctan(b/a) (phase angle)

• Conversion: a = r·cos(θ), b = r·sin(θ)

➕ Addition Rules

Rectangular: (a₁ + jb₁) + (a₂ + jb₂) = (a₁ + a₂) + j(b₁ + b₂)

For polar form, convert to rectangular first

Then convert result back to polar if needed

⚡ AC Applications

Phasors represent sinusoidal voltages and currents

Magnitude represents RMS value

Angle represents phase relationship

🏠 Residential Circuits

Problem: Calculate total current in a parallel AC circuit

Given: I₁ = 10∠0° A, I₂ = 8∠-30° A

Solution: I_total = I₁ + I₂ = 16.93∠-11.77° A

🏭 Industrial Power

Problem: Three-phase power calculation

Given: V_a = 230∠0°, V_b = 230∠-120°, V_c = 230∠120°

Result: Balanced system with zero neutral current

📡 Signal Processing

Application: Combining multiple sinusoidal signals

Example: Audio mixing, RF signal analysis

Benefit: Simplified analysis of complex waveforms

🔌 Power Factor

Concept: Relationship between voltage and current phasors

Formula: PF = cos(θ_v - θ_i)

Importance: Energy efficiency in AC systems