kompleksiarvon

A complex number is a number that can be expressed in the form a + bi, where a and b are real numbers, and i is the imaginary unit, satisfying the equation i² = -1. The term "complex number" is used to denote the set of all complex numbers, typically denoted by the symbol C.

In a complex number, the real number 'a' is called the real part, and the real number 'b' is called the imaginary part. The imaginary unit 'i' is not a real number but a fundamental concept in mathematics. Complex numbers extend the real number system to include solutions to all polynomial equations.

The set of complex numbers can be visualized as a two-dimensional plane, known as the complex plane or Argand plane. The horizontal axis represents the real part, and the vertical axis represents the imaginary part. This geometric representation is useful for understanding operations with complex numbers.

Complex numbers have numerous applications in various fields, including electrical engineering, quantum mechanics, signal processing, and fluid dynamics. They are essential for solving problems that cannot be adequately described by real numbers alone. Operations such as addition, subtraction, multiplication, and division are defined for complex numbers, extending the arithmetic of real numbers. The modulus of a complex number represents its distance from the origin in the complex plane, and the argument represents the angle it makes with the positive real axis.