KEVOS® MAKEOS · Mathematics
Complex Number Calculator
What is the sum, difference, product or quotient of these complex numbers, in rectangular and polar form?
Add, subtract, multiply and divide complex numbers and convert them between rectangular (a + bi) and polar (magnitude and angle) form, for AC circuits, vibration and phasor work.
Open the calculatorRuns in your browser. No account needed.
How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Operation | choice | Operation to perform. |
| z₁ real part | Real part of the first number. | |
| z₁ imaginary part | Imaginary part of the first number. | |
| z₂ real part | Real part of the second number. | |
| z₂ imaginary part | Imaginary part of the second number. |
Method and formulas
- (a + bi)(c + di) = (ac − bd) + (ad + bc)i; (a + bi) ÷ (c + di) = [(ac + bd) + (bc − ad)i] ÷ (c² + d²).
- Polar: magnitude √(re² + im²), angle atan2(im, re).
- Example: (3 + 4i) × (1 -2i) = 11 + -2i.
Limitations
- Angles are reported in degrees from −180° to 180°.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Combine impedances and phasors
- Convert between rectangular and polar form
- Check vibration and control calculations
Who it is for
- Engineers
- Technicians
- Engineering students
What you get
- Result in rectangular form
- Result in polar form
- Polar forms of the inputs
Interpreting the result
- Multiply magnitudes and add angles to check products in polar form.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 18–19. Topic reference; no source tables or recommended settings are reproduced.
WORKOS tools are screening and decision-support utilities. Verify important financial, engineering, safety, legal or operational decisions using appropriate professional standards and your organisation’s approved data.
