Chapter # 2 || Real And Complex Number || EX # 2.6 Q#4
Real numbers are the set of numbers that include all rational and irrational numbers, and can be represented on a number line. Rational numbers are those that can be expressed as the ratio of two integers, while irrational numbers cannot be expressed as a ratio of two integers and have non-repeating, non-terminating decimal expansions. Examples of real numbers include integers, fractions, decimals, and square roots of non-perfect squares.
Complex numbers, on the other hand, are numbers that consist of a real part and an imaginary part, and can be 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. The real part of a complex number corresponds to its position on the real number line, while the imaginary part corresponds to its position on the imaginary axis. Complex numbers can be added, subtracted, multiplied, and divided like real numbers, and can also be represented graphically on a complex plane. The complex plane is a two-dimensional plane with the real axis as the x-axis and the imaginary axis as the y-axis.
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