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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..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 - ..
Subtraction of Matrices
Subtraction of Matrices - Two matrices can be subtracted in the same way as they are added. We change the signs of the corresponding elements and then add them. If then If and , th..
Subtraction of Matrices - Two matrices can be subtracted in the same way as they are added. We change the signs of the corresponding elements and then add them. If then If and , th..Subtraction of Matrices
For two matrices A and B of the same order, we define A-B = A+(-B..
Some properties of Addition and Subtraction of Matrices
(1) A + B = B + A (Commutative property) (2) k(A + B) = kA + kB (Distributive property) (3) (A + B) + C = A + B + C (Distributive property) (4) (A + B) + C = A + (B + C) (Associative property) A + O = O + A = A where O is zero or null matrix. A = A + O (5) A + (-A) = O (-A is additive inverse of A)..
(1) A + B = B + A (Commutative property) (2) k(A + B) = kA + kB (Distributive property) (3) (A + B) + C = A + B + C (Distributive property) (4) (A + B) + C = A + (B + C) (Associative property) A + O = O + A = A where O is zero or null matrix. A = A + O (5) A + (-A) = O (-A is additive inverse of A)..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)).. Result
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