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 where different forms are useful for different operations.

2. How Does the Calculator Work?

The calculator uses the conversion formula:

Where:

• \( x \) — Real part (unitless)
• \( y \) — Imaginary part (unitless)
• \( r \) — Magnitude (unitless)
• \( \theta \) — Angle in radians
• \( i \) — Imaginary unit (√-1)

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

3. Importance of Complex Number Conversion

Details: Rectangular form is better for addition/subtraction, while polar form is better for multiplication/division. Converting between forms allows optimal operations in different contexts.

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.

5. Frequently Asked Questions (FAQ)

Q1: What if my angle is in degrees?
A: Convert degrees to radians first (radians = degrees × π/180) before using this calculator.

Q2: Can I use negative magnitude?
A: No, magnitude (r) must be ≥0. Negative magnitudes can be represented by adding π to the angle.

Q3: What's the range for θ?
A: The angle can be any real number, but typically we use -π to π or 0 to 2π.

Q4: How precise are the results?
A: Results are rounded to 4 decimal places. For exact values, keep symbolic forms.

Q5: What about rectangular to polar conversion?
A: The inverse conversion uses \( r = \sqrt{x^2 + y^2} \) and \( \theta = \arctan(y/x) \).