Rectangular Form Calculator

Turn magnitude and angle into clear rectangular values. Visualize every complex point with steps, exports, graphs, and practical learning support.

Calculator Inputs

Calculation Mode

Magnitude (r)

Angle (θ)

Angle Unit

Real Part (a)

Imaginary Part (b)

Scalar Multiplier

Decimal Precision

Plotly Graph

The graph places your complex number on the Argand plane. It shows the real axis horizontally and the imaginary axis vertically.

Example Data Table

Magnitude	Angle	Unit	Rectangular Form	Real	Imaginary
10	30	Degrees	8.6603 + 5i	8.6603	5.0000
12	120	Degrees	-6 + 10.3923i	-6.0000	10.3923
5	0.7854	Radians	3.5355 + 3.5355i	3.5355	3.5355

Formula Used

Polar to rectangular: z = r(cos θ + i sin θ)

Real part: a = r cos θ

Imaginary part: b = r sin θ

Rectangular form: z = a + bi

Modulus from rectangular values: r = √(a² + b²)

Argument from rectangular values: θ = atan2(b, a)

How to Use This Calculator

Select either Polar to Rectangular or Rectangular Analysis mode.
Enter magnitude and angle for conversion, or enter real and imaginary values for analysis.
Choose degrees or radians when using angular inputs.
Set a scalar if you want to multiply the number before evaluation.
Choose your preferred decimal precision for the output.
Press the calculate button to show the result above the form.
Review the computed form, table, steps, and graph.
Use the export buttons to save the result as CSV or PDF.

Frequently Asked Questions

1. What is rectangular form in complex numbers?

Rectangular form writes a complex number as a + bi. The value a is the real part, and b is the imaginary coefficient.

2. What inputs does this calculator accept?

It accepts polar inputs like magnitude and angle, or rectangular inputs like real and imaginary parts for analysis and verification.

3. Can I use degrees and radians?

Yes. Choose the angle unit before calculating. The tool converts the angle correctly and reports results in both degrees and radians.

4. Why does the result show a negative imaginary part sometimes?

A negative imaginary value means the point lies below the real axis. This commonly happens for angles in Quadrants III and IV.

5. What does the scalar multiplier do?

The scalar multiplies the entered complex quantity before conversion or analysis. It is useful for testing scaled vectors and classroom examples.

6. What is the modulus shown in results?

The modulus is the distance from the origin to the complex point. It represents the magnitude of the number.

7. What does the graph represent?

The graph shows your number on the Argand plane. Horizontal movement is real, and vertical movement is imaginary.

8. Can I export my result for records?

Yes. Use the CSV button for spreadsheet-friendly output or the PDF button for a simple printable report.