positive numbers


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Part I:
When 'n' is any integer, positive or negative then ..
Indices and Laws of Indices
Introduction - If m is a positive integer, a x a x a . m times is written as a m . a is called the base and m is the power. We read it as "a raised to the power m". The power is also called "the index" or "the exponent..
Graphical representation of Complex numbers
The complex number Z = x + iy may be represented graphically by the point P whose rectangular co-ordinates are (x, y). Thus each point in the plane is associated with a complex number. In the figure, P defines Z = x + iy. It is customary to choose x-axis as real axis and y-axi..
Examples:
1, 3, 5, 7..... (adding 2 to every term) 1, 4, 16, 64 (Multiplying by 4 every term) 20, 17, 14 . (add -3 to every term) The different numbers in a sequence are called terms of sequence. The subscripts denote the position of the term. In the second example, 4 is the seco..
Imaginary Number
Square root of a negative number is known as an imaginary number. a > 0 is an imaginary number. or A number whose square is negative is known as an imaginary number. . . . The symbol i, We writ..
Polar form of a Complex number
is called the modulus of the complex number z denoted by |z| and q = tan -1 y/x is called the amplitude or argument of the complex number z denoted by amp(z) or arg(z). The value of q is such that - p < q p , is called the principal value of the amplitude. The general value o..
Introduction
The word 'Induction' means method of reasoning from individual cases to general ones or from observed instances to unobserved ones. Many important mathematical formulae are such that a result is formed by some means which does not provide for a direct proof. Mathematical Induction is a princ..
Examples:
i) A sequence of multiples of 5 5, 10, 15, 20, ii) A sequence of reciprocals of positive integers The above two sequences are clearly the infinite sequence..
Introduction
If m is a positive integer, a x a x a . m times is written as a m . a is called the base and m is the power. We read it as "a raised to the power m". The power is also called "the index" or "the exponent". When the power or index is a fraction say then and it is a surd of order n. In this..
Indices Introduction
Introduction - If m is a positive integer, a x a x a . m times is written as a m . a is called the base and m is the power. We read it as "a raised to the power m". The power is also called "the index" or "the exponent". When the power or index is a fraction say then and it is a surd of o..
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