1. What is Polar to Rectangular Conversion?

The polar to rectangular conversion transforms complex numbers from polar coordinates (magnitude and angle) to rectangular form (real and imaginary components). This is essential in many fields including electrical engineering, physics, and signal processing.

2. How Does the Calculator Work?

The calculator uses the conversion formula:

Where:

• \( x \) — Real component (unitless)
• \( y \) — Imaginary component (unitless)
• \( r \) — Magnitude (unitless)
• \( \theta \) — Angle in radians
• \( i \) — Imaginary unit

Explanation: The formula converts polar coordinates to Cartesian coordinates using trigonometric functions.

3. Importance of Complex Number Conversion

Details: Polar form is often better for multiplication/division of complex numbers, while rectangular form is better for addition/subtraction. Converting between forms is crucial for solving complex number problems.

4. Using the Calculator

Tips: Enter magnitude (must be ≥0) and angle in radians. The calculator will output the real (x) and imaginary (y) components of the complex number.

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between polar and rectangular forms?
A: Polar form uses magnitude and angle, while rectangular form uses real and imaginary components.

Q2: How do I convert degrees to radians?
A: Multiply degrees by π/180. Many calculators have a degree-to-radian conversion function.

Q3: Can I use negative magnitudes?
A: No, magnitude (r) must be ≥0. Negative values would be represented by adding π to the angle.

Q4: What fields use this conversion?
A: Electrical engineering (AC circuits), physics (wave equations), control systems, and signal processing.

Q5: How precise are the results?
A: Results are accurate to 4 decimal places, sufficient for most practical applications.