1. What is Magnitude and Phase Angle?

The magnitude and phase angle are fundamental properties of complex numbers. The magnitude represents the distance from the origin in the complex plane, while the phase angle represents the direction from the positive real axis.

2. How Does the Calculator Work?

The calculator uses the following formulas:

Where:

• \( Re \) — Real part of the complex number
• \( Im \) — Imaginary part of the complex number
• \( \text{atan2} \) — Two-argument arctangent function that returns the correct quadrant

Explanation: These formulas convert a complex number from rectangular coordinates (Re, Im) to polar coordinates (magnitude, phase).

3. Importance of Magnitude and Phase Calculation

Details: Magnitude and phase calculations are essential in signal processing, electrical engineering, physics, and many other fields where complex numbers are used to represent waveforms, impedances, and other physical quantities.

4. Using the Calculator

Tips: Enter the real and imaginary parts of your complex number. The calculator will compute both the magnitude and phase angle in radians.

5. Frequently Asked Questions (FAQ)

Q1: What is the range of the phase angle?
A: The phase angle typically ranges from -π to π radians (-180° to 180°).

Q2: How is atan2 different from atan?
A: atan2 takes two arguments (y, x) and returns the angle in the correct quadrant, while atan(y/x) can only return values between -π/2 and π/2.

Q3: Can I get the phase in degrees instead of radians?
A: To convert from radians to degrees, multiply by 180/π (approximately 57.2958).

Q4: What if both real and imaginary parts are zero?
A: The magnitude would be 0, but the phase angle is undefined for the zero complex number.

Q5: Where are these calculations used in real applications?
A: These calculations are used in electrical engineering for impedance analysis, in signal processing for Fourier analysis, and in physics for wave representation.