1. What is Polar Form Conversion?

The polar form conversion transforms a complex number from rectangular coordinates (a + bi) to polar coordinates (r∠θ). This representation is often more convenient for multiplication, division, and exponentiation of complex numbers.

2. How Does the Calculator Work?

The calculator uses the following equations:

Where:

• \( a \) — Real part of complex number
• \( b \) — Imaginary part of complex number
• \( r \) — Magnitude (always non-negative)
• \( \theta \) — Angle in radians (-π to π)

Explanation: The magnitude represents the distance from origin in complex plane, while the angle represents the direction from positive real axis.

3. Importance of Polar Form

Details: Polar form is essential in electrical engineering (phasors), signal processing, and quantum mechanics. It simplifies complex number operations and provides geometric interpretation.

4. Using the Calculator

Tips: Enter real and imaginary parts of your complex number. The calculator will compute magnitude (always positive) and angle in radians (-π to π).

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between atan and atan2?
A: atan2(b,a) is preferred as it handles all quadrants correctly and accounts for a=0 cases, unlike atan(b/a).

Q2: How do I convert back to rectangular form?
A: Use \( a = r\cos(\theta) \) and \( b = r\sin(\theta) \) to convert polar back to rectangular form.

Q3: What if my complex number is zero?
A: For 0+0i, r=0 but θ is technically undefined (calculator will show 0).

Q4: Can I get the angle in degrees?
A: Multiply radians by (180/π) to convert to degrees. The calculator shows radians as it's the standard mathematical unit.

Q5: Why is polar form useful?
A: It simplifies multiplication (multiply magnitudes, add angles) and division (divide magnitudes, subtract angles) of complex numbers.