1. What is Polar to Rectangular Conversion?

The polar to rectangular conversion transforms complex numbers from polar form (r, θ) to rectangular form (x + yi). This is essential in engineering, physics, and mathematics when working with complex numbers in different coordinate systems.

2. How Does the Calculator Work?

The calculator uses the conversion formula:

Where:

• \( r \) — Magnitude (distance from origin)
• \( \theta \) — Angle in radians
• \( x \) — Real component
• \( y \) — Imaginary component
• \( i \) — Imaginary unit (√-1)

Explanation: The formula converts polar coordinates (magnitude and angle) to Cartesian coordinates (x and y components).

3. Importance of Complex Number Conversion

Details: Different mathematical operations are easier in different forms. Polar form is better for multiplication/division, while rectangular form is better for addition/subtraction.

4. Using the Calculator

Tips: Enter the magnitude (must be ≥0) and angle in radians. The calculator will output the rectangular form x + yi.

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 x (real) and y (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: Magnitude (r) should be ≥0. Negative magnitudes can be handled by adding π to the angle.

Q4: What are typical applications of this conversion?
A: Used in electrical engineering (phasors), signal processing, control systems, and quantum mechanics.

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