rainwyz0706 said:I can write it as the sum of (z^n)*(1+w^n+w^2n)/n!, n from 0 to infinity. But I'm still not sure how to simplify 1+w^n+w^2n from 1+w+w^2=0. Could you explain it in a bit more details? Thanks a lot!
A complex number is a number that is expressed in the form a + bi, where a and b are real numbers and i is the imaginary unit, defined as the square root of -1. Complex numbers are commonly used in mathematics and physics to represent quantities that have both real and imaginary components.
A real number is a number that can be expressed on a number line, and includes all positive and negative numbers as well as zero. A complex number, on the other hand, has both a real and an imaginary component and cannot be represented on a number line. In other words, a complex number is a superset of real numbers.
A power series is an infinite series in the form of a polynomial, where the coefficients of the terms increase in a specific pattern. It is commonly used in calculus to represent a function as an infinite sum of simpler functions. Power series are also useful for approximating functions and solving differential equations.
Complex numbers can be used to represent the coefficients in a power series, allowing for the representation of complex functions. Power series can also be used to approximate complex functions, making them an important tool in the study of complex numbers.
Complex numbers and power series are used in a variety of fields, including electrical engineering, physics, and signal processing. They are used in the study of alternating current circuits, quantum mechanics, and Fourier analysis, among others. They are also used in computer graphics and animation to create 3D effects.