The Geometry of Magnitude
It's the length of the vector, derived from a classic theorem.
The magnitude (or modulus) of a complex number z = a + bi is its distance from the origin (0,0) on the complex plane. As our calculator's visualizer shows, the real part (a) and the imaginary part (b) form the two legs of a right-angled triangle.
The magnitude, represented as |z|, is the hypotenuse of this triangle. Therefore, its value is calculated using the Pythagorean theorem: |z| = √(a² + b²). This fundamental property is essential for measuring vector lengths in physics, signal processing, and engineering.
An Instrument of Clarity
Features designed to make complex concepts intuitive and clear.
Live Blueprint Visualizer
Our unique graph doesn't just plot a point—it draws the underlying Pythagorean triangle, providing a clear, geometric understanding of how the magnitude is derived.
Specification Block Output
The result isn't just a number. It's presented in a technical specification block that reinforces the formula, creating a clean, professional, and educational output.
Instantaneous Calculation
Modify the real or imaginary parts and watch the magnitude and blueprint update in real-time. This provides instant feedback for rapid exploration and analysis.
A Two-Step Process
From input to insight in seconds.
Enter Components
Input the real part (a) and the imaginary part (b) of your complex number into the clean, minimalist fields.
Review the Output
Instantly see the calculated magnitude in the spec block and observe the corresponding vector and triangle on the blueprint graph.
