Unlock the Secrets of Complex Logarithms
Dive into the fascinating world of complex numbers and calculate logarithms with ease. Visualize the results on the complex plane!
Enter Complex Number and Base
To calculate the complex logarithm, provide the real and imaginary parts of your complex number, and the base for the logarithm.
Complex Logarithm Result:
Visualizing Complex Numbers
Explore the complex numbers on the complex plane. Input number on the left, and its logarithm on the right.
Input Number
Complex Logarithm
Understanding Complex Logarithms
The complex logarithm extends the concept of logarithms to complex numbers. For a complex number z = x + iy, and a base b, the complex logarithm logb(z) is a complex number w such that bw = z.
Due to the periodic nature of complex exponentials, the complex logarithm is multi-valued. This calculator provides the principal value of the complex logarithm.
Formula: If z = reiθ is the polar form of a complex number, then logb(z) = logb(r) + i(θ + 2πk) / ln(b), for any integer k. For the principal value, we take k = 0 and the principal value of θ in the interval (-π, π].
Use this tool to explore complex logarithms and visualize their representation on the complex plane.