To represent an irrational number on the number line
. Then, the point P represents on the number line. Using Pythagoras' theorem in rt. OB = , if AO = 2 and AB = 1 Cut off OP = OB = Then the point P represents on the number line. In the same w..
. Then, the point P represents on the number line. Using Pythagoras' theorem in rt. OB = , if AO = 2 and AB = 1 Cut off OP = OB = Then the point P represents on the number line. In the same w..Complex number
Square root of a negative number is known as an imaginary number . 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 following ar..
Geometrical Representation of Complex Number
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 ..
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 ..Irrational Numbers
) It is not possible to find the exact value of an irrational number. (iii) All rational and irrational numbers can be marked on the number line. Write two possible irrational numbers between 2 and 3. Consider the squares..
) It is not possible to find the exact value of an irrational number. (iii) All rational and irrational numbers can be marked on the number line. Write two possible irrational numbers between 2 and 3. Consider the squares..Summary
1. Problems involving rational numbers are simplified using 'BODMAS' rule. 2. A rational number can be represented in the decimal form. 3. When a rational number is represented as a decimal, it will be either a terminatin..
Cube roots of unity
where 2n p + 0 is the general amplitude. when n=0, z = cos 0 + i sin 0=1 \ The cube roots of unity are which are usually denoted by 1, w, w 2 ..
where 2n p + 0 is the general amplitude. when n=0, z = cos 0 + i sin 0=1 \ The cube roots of unity are which are usually denoted by 1, w, w 2 ..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 q /q and others are uniformly spaced around the circle separated from others by an angle 2p ..
To represent a rational number on the number line
Mark the following rationals on the number line: ..
Mark the following rationals on the number line: ..Example 2:
The following are examples of an infinite set. Set of all points on a line segment of 2cm. Set of all similar triangles in a plane. Set of rational numbers between the integers 1 and 2 {x : x I and x > 2} {x: x is an even number..
Properties of Symmetric and Skew Symmetric Matrices
1. A square matrix A is said to be skew-symmetric if A ' = -A. 2. The diagonal elements of a skew-symmetric matrix are all ze..
Result
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