Complex numbers are numbers that are expressed in the form a + bi, where a and b are real numbers and i is the imaginary unit (√-1). They are different from real numbers because they have both a real part (a) and an imaginary part (bi).
Imaginary numbers allow us to work with and solve problems that cannot be solved with real numbers alone. They are essential in many fields of mathematics, including complex analysis, number theory, and physics.
Imaginary numbers cannot be visualized in the same way as real numbers can be represented on a number line. However, they can be represented as points on a complex plane, where the real part is plotted on the x-axis and the imaginary part on the y-axis.
Complex numbers have many practical applications, such as in electrical engineering, signal processing, and quantum mechanics. They can also be used to solve problems in areas such as fluid dynamics, heat transfer, and optimization.
In addition to real numbers, complex algebra involves working with imaginary numbers and their properties. This includes operations such as addition, subtraction, multiplication, and division of complex numbers. Regular algebra only deals with real numbers.