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Introduction
The sets of numbers which every student must remember are: The set of natural numbers, The set of whole numbers, The set of integers, The set of rational numbers, The set of irrational numbers, Set of Real Numbers, Consecut..
Argand diagram of the qth roots of a Complex number
All the q-th roots of z lie on a circle centred at the origin O and having radius equal to the real, positive q t h root of r. One of them has amplitude and others are uniformly spaced around the circle separated from others by an ang..
Properties of Transpose
(A T ) T = A (A + B) T = A T + B T , A and B being of the same order. (KA) T = KA T , k be any scalar (real or complex) (AB) T = B T A T ; A and B being conformable for the product A..
Additive identity of the Complex number
The complex number 0 + i0 is the additive identity for the set of complex numbers. 0 + i0 is called the additive identity for the complex number. Z + (0 + i 0 ) = a + i b + (0 + i 0) = (a + 0) + i (b + 0) = a + i..
Conjugate complex numbers
If Z = a + ib is a complex number, then a - ib is called the complex conjugate of a + ib and the conjugate is denoted by..
If Z = a + ib is a complex number, then a - ib is called the complex conjugate of a + ib and the conjugate is denoted by..Greatest Common Factor and Least Common Multiple
The greatest of the common divisors of two or more than two numbers is called the GCD or HCF (Highest Common Factor). The least common multiple of two or more than two numbers is called the L..
Compounded ratio
If two or more ratios are multiplied term-wise, the ratio thus formed is called their compounded rati..
Definition of ratio
If a and b are two quantities with the same units such that b is not equal to zero; then the quotient a/b is called the ratio between a and b. It is written as a:b. Ratio does not have any unit. The quantities a and b are called terms of the ratio. a' is called a..
Singleton Set or Singlets
A set consisting of a single element is called a singleton set or singlet. The cardinality of the singleton set is ..
Exponential form of a Complex number
If z = x + iy then e z = e (x + iy) = e x e iy ? e z = e x {cos y + i sin y} is called the Exponential form of the Complex number..
Result
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