Enter a complex number to find its angle (argument).
The Angle of a Complex Number
Discover the core concept behind the calculation.
A complex number, expressed as z = a + bi, is more than just an algebraic term; it represents a point (a, b) on a two-dimensional grid known as the complex plane. The horizontal axis is the 'Real' axis, and the vertical axis is the 'Imaginary' axis.
The angle (θ), or argument, is the angle formed between the positive Real axis and the vector connecting the origin (0,0) to the point (a,b). This value is crucial in understanding the number's phase and is fundamental in fields like electrical engineering, physics, and advanced mathematics. Our tool calculates this using the atan2(b, a) function for accuracy across all quadrants.
An Instrument of Precision
Engineered with features that enhance understanding and workflow.
Live Visualizer
Instantly see your complex number plotted on the complex plane. The interactive graph provides immediate visual feedback, connecting the numbers to their geometric representation.
Dual Unit Output
Get the angle in both Degrees and Radians simultaneously. The elegant dials provide a quick visual reference, perfect for both academic and practical applications.
Real-Time Updates
No 'calculate' button needed. The results and the graph update instantly as you type, allowing for rapid exploration and analysis of different complex numbers.
Simple & Intuitive Operation
Get your results in two straightforward steps.
Input Your Values
Enter the real part (a) and the imaginary part (b) of your complex number into the designated input fields.
Read the Results
Instantly view the calculated angle on the dials and see the number visualized on the interactive complex plane graph.
