1. What is Exponential to Rectangular Conversion?

The exponential form (r·e^(iθ)) and rectangular form (a + bi) are two ways to represent complex numbers. This calculator converts between these forms, which is essential in electrical engineering, physics, and signal processing.

2. How Does the Calculator Work?

The calculator uses Euler's formula:

Where:

• \( r \) — Magnitude (absolute value) of the complex number
• \( θ \) — Angle (in radians) of the complex number
• \( a \) — Real part (a = r·cosθ)
• \( b \) — Imaginary part (b = r·sinθ)

Explanation: The exponential form represents a complex number using its magnitude and angle, while the rectangular form uses its real and imaginary components.

3. Importance of Complex Number Forms

Details: Different forms are useful for different operations. Exponential form simplifies multiplication and division, while rectangular form is better for addition and subtraction.

4. Using the Calculator

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

5. Frequently Asked Questions (FAQ)

Q1: How do I convert degrees to radians?
A: Multiply degrees by π/180. Most programming languages have a deg2rad() function.

Q2: What's the difference between polar and exponential form?
A: Polar form is r(cosθ + i sinθ), which is equivalent to the exponential form re^(iθ) by Euler's formula.

Q3: Can I use this for vectors?
A: Yes, complex numbers can represent 2D vectors, where the real part is x-component and imaginary part is y-component.

Q4: What if my angle is outside [0, 2π]?
A: The calculator will still work as trigonometric functions are periodic (repeat every 2π).

Q5: How do I convert back to exponential form?
A: r = √(a² + b²), θ = atan2(b, a). We may add this functionality in a future version.