Complex Number to Polar Form Converter
Easily convert complex numbers from rectangular form (a + bi) to polar form (r, θ) online. Visualize complex numbers on the complex plane and understand magnitude and argument.
Enter Complex Number
In rectangular form: \(a + bi\)
Polar Form Result
Magnitude (r):
Argument (θ): radians
Complex Plane Visualization
Understanding Complex to Polar Form Conversion
A complex number can be represented in rectangular form as \(z = a + bi\), where \(a\) is the real part and \(b\) is the imaginary part. The polar form represents the same complex number using a magnitude (or modulus) \(r\) and an argument (or angle) \(\theta\).
Formulas
- Magnitude (r): The distance from the origin to the point \((a, b)\) in the complex plane.
Formula: \( r = \sqrt{a ^ (2 + b) ^ 2} \)
- Argument (θ): The angle between the positive real axis and the line connecting the origin to the point \((a, b)\) in the complex plane, measured in radians.
Formula: \( \theta = \operatorname{atan2}(b, a) \) (using atan2 to handle all quadrants correctly).
How to Use This Converter
Simply enter the real and imaginary parts of your complex number in the input fields provided. Click the "Calculate Polar Form" button to convert and see the magnitude and argument. The complex number will also be visualized on the complex plane for a better understanding. Use the "Reset" button to clear the inputs and results.