Complex Number Exponential Form Converter

Transform complex numbers from rectangular form a + bi to exponential form re^(iθ). Visualize the complex number in the complex plane.

Enter the real and imaginary components of your complex number in rectangular form.

Real Part (a)

Imaginary Part (b)

Result: Exponential Form

Exponential Form:

Magnitude (r):

Angle (θ) in radians:

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!