1. What is Polar to Rectangular Conversion?

The polar to rectangular conversion transforms a complex number from its polar form (r, θ) to rectangular form (a + bi). This is essential in many areas of engineering, physics, and mathematics where complex numbers are used.

2. How Does the Calculator Work?

The calculator uses the conversion formula:

Where:

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

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

3. Importance of Complex Number Conversion

Details: Converting between polar and rectangular forms is crucial for simplifying complex number operations, analyzing AC circuits, signal processing, and solving differential equations.

4. Using the Calculator

Tips: Enter the magnitude (must be ≥0) and angle in radians. The calculator will compute the real (a) and imaginary (b) components of the rectangular form.

5. Frequently Asked Questions (FAQ)

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

Q2: Can I input angle in degrees?
A: This calculator requires radians. Multiply degrees by π/180 to convert.

Q3: What if my magnitude is negative?
A: Magnitude should be ≥0. Negative magnitudes can be handled by adding π to the angle.

Q4: When is polar form more useful?
A: Polar form simplifies multiplication, division, and powers of complex numbers.

Q5: When is rectangular form more useful?
A: Rectangular form simplifies addition, subtraction, and certain integrations.