Matrices and Determinants
Matrices - A rectangular array of entries is called a Matrix. The entries may be real, complex or functions. The entries are also called as the elements of the matrix. The rectangular array of entries are enclosed in an ordinary bracket or in square bracke..
Sequences and Series
Introduction - A set of numbers arranged in a definite order according to some definite rule is called a sequenc..
Example:
A set containing 2,3,5,7,8 is Written as {2,3,5,7,8} in Roster metho..
Sequences and Series
Sequence : A set of numbers arranged in a definite order according to some definite rule is called a sequence.A sequence is a function whose domain is the set N of natural numbers. Series : Indicated sum of the terms in a sequence is called a ..
Summary
Let X be a set of numbers and f : N n --> X be a function, then the ordered set {f(1), f(2),...., f(n)} is called a finite sequence in X...
Proof:
The null set f is a subset of every set, in particular f A. By hypothesis, A f . The two conditions imply A = f..
qth root complex number Argand diagram
Argand diagram of the q th roots of a Complex number - All the q-th roots of z lie on a circle centred at the origin O and having radius equal to the real, positive q t h root of r. One of them has amplitude and others are uniformly spaced around the circle separated from others..
Argand diagram of the q th roots of a Complex number - All the q-th roots of z lie on a circle centred at the origin O and having radius equal to the real, positive q t h root of r. One of them has amplitude and others are uniformly spaced around the circle separated from others..De Moivre's Theorem
De Moivre's formula, named after Abraham de Moivre, states that for any complex number (and, in particular, for any real number) x and any integer n it holds that The formula is important because it connects complex numbers (i stands for the imaginary..
De Moivre's formula, named after Abraham de Moivre, states that for any complex number (and, in particular, for any real number) x and any integer n it holds that The formula is important because it connects complex numbers (i stands for the imaginary..Argand diagram of the qth roots of a Complex number All the q-th roots of z lie on a circle centred at the origin O and having radius equal to the real, positive q t h root of r. One of them has amplitude and others are uniformly spaced around the circle separated from others by an ang..
All the q-th roots of z lie on a circle centred at the origin O and having radius equal to the real, positive q t h root of r. One of them has amplitude and others are uniformly spaced around the circle separated from others by an ang..Definition:
Union of two sets A and B is the set of all elements which are in A, or in B, or both in A and B. In Set builder form,..
Union of two sets A and B is the set of all elements which are in A, or in B, or both in A and B. In Set builder form,..See what our Users say :
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