Statement of DeMoivre's Theorem
If 'n' be any rational number, positive or negative, the..
If 'n' be any rational number, positive or negative, the..Remember:
If the middle term is negative, and last term is positive, signs of both the factors will be 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,..
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..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..Negative of a Complex number
If Z = a + ib, then Z is called the negative of Z. -Z = -(a + ib) = -a - ..
Middle Terms for Positive Integral Index
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..
General Term for Positive Integral Index
General Term for Positive Integral Index is: For 0 r n, we have T r + 1 = n C r a n - r b r..
General Term for Positive Integral Index is: For 0 r n, we have T r + 1 = n C r a n - r b r..Greatest Terms for Positive Integral Index
Greatest Terms for Positive Integral Index - In (a + b) n , let 'a' and 'b' be both positive numbers. As r increases, the factor decreases. So long as this factor is greater than 1, T r..
Greatest Terms for Positive Integral Index - In (a + b) n , let 'a' and 'b' be both positive numbers. As r increases, the factor decreases. So long as this factor is greater than 1, T r..Greatest Terms for Positive Integral Index
Working rules for finding the greatest term: Step 1: In (a + b) n , the constants a and b must be positive. Step 2: Write T r+1 and T r and find the value of T r+1 /T r . Step 3: Simplify the inequality (T r+1 /T r ) greater than or equal to 1 and find the..
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