Business Mathematics | Chapter 1 | Number System | A+iB

Business Mathematics | Chapter 1 | Number System | A+iB | Class 06

Rasel Bhuiyan
Teacher | Founder & CEO BBA WORLD 365
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Rasel Sir: 01675289476 (WhatsApp - Only Text)

Number System: Introduction, Prime, Rational and Irrational number, even and odd numbers and their properties. Imaginary and complex numbers; sequence, series, Divergence of a sequence, sigma notation, Sum of natural numbers Number System: A number system is a mathematical notation for representing numbers. It includes a set of digits and rules for combining those digits to represent quantities. The most common number systems are the decimal system (base 10), binary system (base 2), octal system (base 8), and hexadecimal system (base 16). Rational Number: A rational number is any number that can be expressed as a fraction p/q, where p and q are integers (whole numbers) and q is not equal to 0. In other words, a rational number is a number that can be written as the ratio of two integers. Rational numbers include integers, fractions, and terminating or repeating decimals. For example, 2, -5, 1/2, and 0.75 are all rational numbers. Irrational Number: An irrational number is a number that cannot be expressed as a simple fraction p/q, where p and q are integers, and q is not equal to 0. Irrational numbers have non-repeating, non-terminating decimal expansions. The decimal expansion of an irrational number goes on forever without settling into a repeating pattern. Examples of irrational numbers include the square root of 2 (√2), pi (π), and the golden ratio (φ). Complex Number: A complex number is a number that can be written 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. The real part of the complex number is "a," and the imaginary part is "bi." Complex numbers extend the real number system to include numbers that cannot be represented on the real number line alone. They are used extensively in various mathematical and scientific applications. Imaginary Number: An imaginary number is a number that is a real multiple of the imaginary unit "i." Imaginary numbers are written in the form bi, where "b" is a real number. They are a subset of complex numbers and are used to represent quantities that involve the square root of -1 in mathematical equations. Imaginary numbers are essential in fields like engineering, physics, and mathematics. Complex numbers are formed by combining real and imaginary parts, and they provide a way to represent and manipulate quantities involving both real and imaginary components. The number system hierarchy goes from natural numbers to integers, rational numbers, irrational numbers, real numbers, and finally complex numbers.

The complex number is basically the combination of a real number and an imaginary number. The complex number is in the form of a+ib, where a = real number and ib = imaginary number. Also, a,b belongs to real numbers and i = √-1.
Hence, a complex number is a simple representation of addition of two numbers, i.e., real number and an imaginary number. One part of it is purely real and the other part is purely imaginary.

#a+ib #complexnumbers

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