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Remember:
If the middle term is positive, and the last term is negative, the sign of one of the factors is positive and the other is negative..
Factorization of trinomials
The general form of the trinomial is (x 2 + cx + d) where c and d have different numerical values: c = a + b, and d = ab. In the given trinomial expression if all terms are positive, then both the factors are positive. If the middle term is negative,..
Part I:
When 'n' is any integer, positive or negative then ..
When 'n' is any integer, positive or negative then ..Complex number
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 write, P..
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 write, P..Examples:
From the two examples it is seen that the signs of the terms of a GP must either be all alike or alternatively positive and negative. Note that the numbers in continued proportion are in GP, i.e.,..
From the two examples it is seen that the signs of the terms of a GP must either be all alike or alternatively positive and negative. Note that the numbers in continued proportion are in GP, i.e.,..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..
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..Expansions for Positive Integral Index
Some particular expansions for Positive Integral Index - For n N, we have: a) (a - b) n (a +(- b))..
Some particular expansions for Positive Integral Index - For n N, we have: a) (a - b) n (a +(- b))..Middle Terms for Positive Integral Index
The number of terms in the expansion of (a + b) n depends on the index n. The index n is either even or o..
Particular Terms for Positive Integral Index
Particular Terms for Positive Integral Index - Sometimes, a particular term satisfying certain conditions is required in the binomial expansion of the type (a + b) n . This can be done by expanding (a + b) n and then locating the required term. Generally this becomes a tedious task, speci..
Middle Terms for Positive Integral Index
The number of terms in the expansion of (a + b) n depends on the index n. The index n is either even or od..
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