1. What is Trigonometric Form?

The trigonometric form (also called polar form) of a complex number represents it in terms of its magnitude and angle. It's expressed as z = r (cos θ + i sin θ), where r is the magnitude and θ is the angle in radians.

2. How Does the Calculator Work?

The calculator uses the trigonometric form equation:

Where:

• \( r \) — Magnitude (always non-negative)
• \( \theta \) — Angle in radians
• \( i \) — Imaginary unit (√-1)

Explanation: The calculator converts the polar form to both trigonometric representation and rectangular form (a + bi).

3. Importance of Trigonometric Form

Details: Trigonometric form is particularly useful for multiplying, dividing, and raising complex numbers to powers (via De Moivre's Theorem). It simplifies many operations in complex analysis.

4. Using the Calculator

Tips: Enter the magnitude (must be positive) and angle in radians. The calculator will display both the trigonometric form and the equivalent rectangular form.

5. Frequently Asked Questions (FAQ)

Q1: How is this different from rectangular form?
A: Rectangular form uses x + yi notation, while trigonometric form uses magnitude and angle, which is often more convenient for certain operations.

Q2: Can I use degrees instead of radians?
A: This calculator requires radians, but you can convert degrees to radians by multiplying by π/180.

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

Q4: How is r related to the complex number?
A: r is the distance from the origin to the point in the complex plane (√(a² + b²) in rectangular form).

Q5: What's Euler's formula connection?
A: The trigonometric form can also be written as z = re^(iθ) using Euler's formula.