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 particularly useful for multiplication, division, and exponentiation of complex numbers.

2. How Does the Calculator Work?

The calculator uses the following formulas:

Where:

• \( a \) — Real part of complex number
• \( b \) — Imaginary part of complex number
• \( r \) — Magnitude (absolute value)
• \( \theta \) — Angle in radians (argument)
• \( i \) — Imaginary unit

Explanation: The calculator converts from rectangular form (a + bi) to trigonometric form (r(cosθ + i sinθ)).

3. Importance of Trigonometric Form

Details: Trigonometric form simplifies complex number operations, especially multiplication (multiply magnitudes, add angles) and division (divide magnitudes, subtract angles).

4. Using the Calculator

Tips: Enter the real and imaginary parts of your complex number. The calculator will compute the magnitude and angle, then display the trigonometric form.

5. Frequently Asked Questions (FAQ)

Q1: Why use trigonometric form?
A: It's more convenient for certain operations like multiplication, division, and finding powers/roots of complex numbers.

Q2: How is θ different in degrees vs radians?
A: This calculator uses radians. To convert to degrees, multiply by 180/π.

Q3: What's the range for θ?
A: The angle θ is typically between -π and π radians (-180° to 180°).

Q4: What if my complex number is zero?
A: For z = 0, r = 0 and θ is undefined.

Q5: Can I convert back to rectangular form?
A: Yes, using a = r cosθ and b = r sinθ.