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Complex Number to Rectangular Form Calculator.

Convert modulus and angle to rectangular components.

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01

Set your values

Results update as you type.

Real part: 3

Real part

3.000000
Imaginary part: 4

Imaginary part

4.000000

Results update automatically as you type.

Use Cases

Convert polar to rectangular for circuit analysis

In AC circuit analysis, voltages and currents are often given as magnitudes and phase angles. Use this calculator to convert them to rectangular form for easier addition and subtraction.

Example: Convert 10∠30° to rectangular form: 8.66 + 5i

Convert polar to rectangular for physics problems

When dealing with vectors or wave functions, converting from polar to rectangular coordinates helps in resolving components along axes.

Example: Convert a force of 50 N at 60° to its x and y components.

Frequently Asked Questions

How do I convert a complex number from polar to rectangular form?
Enter the modulus (r) and the angle (θ) in degrees. The calculator computes the real part as r*cos(θ) and the imaginary part as r*sin(θ), giving you the rectangular form a + bi.
What is the rectangular form of a complex number?
The rectangular form is a + bi, where 'a' is the real part and 'b' is the imaginary part. It represents the coordinates on the complex plane, with 'a' on the horizontal axis and 'b' on the vertical axis.
Can I use this calculator for angles in radians?
No, this calculator expects the angle in degrees. If you have an angle in radians, convert it to degrees first (multiply by 180/π) before entering it.

Tips & Common Mistakes

Tips

  • Ensure the angle is in degrees, not radians, before entering it.
  • The modulus must be a non-negative number. If you have a negative modulus, take its absolute value and adjust the angle by 180°.
  • Use the rectangular form to easily add or subtract complex numbers, as you simply combine real and imaginary parts separately.
  • Double-check your angle measurement: angles in the second and third quadrants will have negative real or imaginary parts.

Common Mistakes to Avoid

  • Forgetting to convert radians to degrees, leading to incorrect results.
  • Entering the angle in the wrong unit (e.g., using gradians instead of degrees).
  • Misinterpreting the sign of the imaginary part when the angle is in the fourth quadrant (negative angle).

Last updated: August 13, 2026