negatives and positive numbers

If 'n' be any rational number, positive or negative, the..

If the middle term is negative, and last term is positive, signs of both the factors will be negative..

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.,..

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..

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..

If Z = a + ib, then Z is called the negative of Z. -Z = -(a + ib) = -a - ..

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 is: For 0 r n, we have T r + 1 = n C r a n - r b 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..

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..