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Some important results
Given a, b, c and d are non-zero real numbers, we can deduce other proportions by simple Algebra. These results are often referred by the names mentioned along each of the properties obtained. (1) If then bc = ad This property is known as INVERTENDO. (2) If , then ad = bc This p..
Given a, b, c and d are non-zero real numbers, we can deduce other proportions by simple Algebra. These results are often referred by the names mentioned along each of the properties obtained. (1) If then bc = ad This property is known as INVERTENDO. (2) If , then ad = bc This p..Real Numbers
The union of the set of rational numbers and irrational numbers forms the set of real numbers. (i) For every real number, there is a corresponding point on the number line. (ii) For every point on the number line,..
Real Numbers
The union of the set of rational numbers and irrational numbers forms the set of real numbers. Q = {rational numbers} = {irrational numbers} Then = R = {real numbers..
The union of the set of rational numbers and irrational numbers forms the set of real numbers. Q = {rational numbers} = {irrational numbers} Then = R = {real numbers..Note:
Set of real numbers is a proper subset of the set of Complex numbers..
Introduction
This chapter takes us much further and adds to our already existing knowledge about Ratio and Proportion. We will have to use many of the algebraic manipulations learnt earlier, use them with expertise to solve problems in this chapt..
Complex Numbers
If x and y are real numbers, then x + iy is called a complex number. x is called the real part and y is called the imaginary part. The complex number x + iy is also written as an ordered pair (x, y) and is denoted by z. i.e., z = x + iy The positive..
If x and y are real numbers, then x + iy is called a complex number. x is called the real part and y is called the imaginary part. The complex number x + iy is also written as an ordered pair (x, y) and is denoted by z. i.e., z = x + iy The positive..Equality of Complex numbers
Two complex numbers are equal iff their corresponding real parts and imaginary parts are separately equal..
Two complex numbers are equal iff their corresponding real parts and imaginary parts are separately equal..Geometrical representation of a Complex number, Argand diagram
Since every complex number z = x + iy is an order pair of real numbers (x, y), it can therefore be represented by a point P(x,y) in the xy plane by taking the real part along the x-axis and the imaginary part along the y-axis. This representation of a ..
Since every complex number z = x + iy is an order pair of real numbers (x, y), it can therefore be represented by a point P(x,y) in the xy plane by taking the real part along the x-axis and the imaginary part along the y-axis. This representation of a ..Ratio and Proportion II
Introduction - This chapter takes us much further and adds to our already existing knowledge about Ratio and Proportion. We will have to use many of the algebraic manipulations learnt earlier, use them with expertise to solve problems in this chapte..
Addition of Matrices
To add two matrices: (i) Check whether they are of the same order. (ii) If they are of the same order, add the corresponding elements. (ii) It will be seen that the matrix obtained after addition will also be a matrix of the same orde..
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