Complex Number Exponential Form Converter
Easily convert complex numbers from rectangular form to exponential form online. Visualize complex numbers and understand the conversion process with this free tool.
Enter the real and imaginary components of your complex number in rectangular form.
Result: Exponential Form
Complex Number Visualization
Understanding Complex Number Exponential Form
A complex number can be represented in rectangular form as a + bi, where a is the real part and b is the imaginary part. Alternatively, it can be expressed in exponential form as re^(iθ), where r is the magnitude (or modulus) and θ is the angle (or argument) in radians.
The magnitude r is the distance from the origin to the point (a, b) in the complex plane, calculated as r = √(a² + b²). The angle θ is the angle between the positive real axis and the line connecting the origin to (a, b), calculated as θ = arctan(b/a).
This converter tool simplifies the process of converting between these forms, providing a visual representation to enhance understanding. Use it to explore complex numbers in a new light!