Quadratic Equation Solver (ax² + bx + c = 0)
About Absolute Value Calculator
The Absolute Value ($|x|$) & Complex Modulus Calculator computes non-negative magnitude for real numbers, integers, vectors, and complex numbers ($|a + bi| = \sqrt{a^2 + b^2}$) with distance-from-zero geometric visualization.
How to Use Absolute Value Calculator
Step 1
Enter a real number, fraction, or complex number (e.g. `-142.5` or `5 + 12i`).
Step 2
Review computed absolute value, distance from zero, and polar coordinates.
Step 3
Click "Copy Absolute Value".
Practical Use Cases for Absolute Value Calculator
Calculating Signal Amplitude & Complex Number Magnitudes
Compute phasor magnitudes and Euclidean lengths for complex impedance vectors ($Z = R + jX$) in AC circuit theory.
Error Tolerance & Absolute Difference Analysis
Calculate absolute error margins ($|\text{Actual} - \text{Theoretical}|$) and deviation bounds in experimental scientific data.
Input & Output Examples
Calculating Absolute Value of Complex Number
Complex Number: `3 - 4i`
Modulus / Magnitude: `|3 - 4i| = \sqrt{3^2 + (-4)^2} = \sqrt{25} = 5.0` | Phase Angle: `-53.13° (-0.927 rad)`Key Features & Performance
- ✓Computes absolute values for Real Numbers, Fractions, and Complex Numbers ($a + bi$).
- ✓Calculates Euclidean vector norms ($||\vec{v}|| = \sqrt{x^2 + y^2 + z^2}$) in 2D, 3D, and N-D space.
- ✓Interactive number line visualizer showing geometric distance from origin (0).
- ✓100% Client-Side memory execution.
- ✓1-Click Copy computed absolute value.
Key Terminology & Definitions
Absolute Value ($|x|)$
The non-negative numerical value of a real number without regard to its sign ($|x| = x$ if $x \ge 0$, $|x| = -x$ if $x < 0$).
Complex Modulus
The distance of a complex number $z = a + bi$ from the origin in the complex plane, defined as $|z| = \sqrt{a^2 + b^2}$.