Complex Number Power Calculator
Unleash the power of complex numbers! Calculate (a + bi)^n and visualize it on the complex plane.
Enter Complex Number (z = a + bi)
Enter Power (n)
Result: zn =
Complex Plane Visualization
Understanding Complex Number Power
Complex numbers are numbers of the form a + bi, where a is the real part, b is the imaginary part, and i is the imaginary unit (i² = -1). Raising a complex number to a power involves multiplying the complex number by itself a certain number of times.
Formula: To calculate (a + bi)^n, we use De Moivre's Theorem or binomial expansion for integer powers. For real powers, it involves converting to polar form, raising the modulus to the power, and multiplying the argument by the power.
Use Cases: Complex number powers are crucial in various fields like electrical engineering (AC circuit analysis), quantum mechanics, signal processing, and fractal generation (like Mandelbrot set). They help in solving problems involving oscillations, rotations, and wave phenomena.
Learn more about complex numbers and their powers on resources like Wikipedia and math textbooks.