Complex Numbers
Square root of a negative number is known as an imaginary number . If x and y are real numbers, then x + iy is called a complex number . x is called the real part and y is called the imaginary part . The following ar..
Sub-duplicate Ratio:
The ratio obtained by taking the square root of the given ratio a:b is called the sub-duplicate ratio. is the sub-duplicate ratio of a : b. For example, the sub-duplicate ratio of 4 : 9 is or 2 :..
The ratio obtained by taking the square root of the given ratio a:b is called the sub-duplicate ratio. is the sub-duplicate ratio of a : b. For example, the sub-duplicate ratio of 4 : 9 is or 2 :..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 writ..
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 writ..Cube roots of unity
where 2n p + 0 is the general amplitude. when n=0, z = cos 0 + i sin 0=1 \ The cube roots of unity are which are usually denoted by 1, w, w 2 ..
where 2n p + 0 is the general amplitude. when n=0, z = cos 0 + i sin 0=1 \ The cube roots of unity are which are usually denoted by 1, w, w 2 ..Representation of fourth roots of unity
radius = ..
radius = ..To find the qth roots of a Complex number
One of the most important applications of De Moivre's theorem is to find the q t h roots of a complex number. Let z = x + iy be a complex number. Let z = r {cos q + i sin q } be its polar form. And z 1/q be the q th root of z. T..
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 q /q and others are uniformly spaced around the circle separated from others by an angle 2p ..
To find the qth roots of a Complex number
One of the most important applications of De Moivre's theorem is to find the q t h roots of a complex number. Let z = x + iy be a complex number. Let z = r {cos q + i sin q } be its polar form. We have z = r {cos(2n p + q ) + i sin (2n p + q )} [2n p + q is the general..
One of the most important applications of De Moivre's theorem is to find the q t h roots of a complex number. Let z = x + iy be a complex number. Let z = r {cos q + i sin q } be its polar form. We have z = r {cos(2n p + q ) + i sin (2n p + q )} [2n p + q is the general..Inverse of a Square Matrix
Let A be a square matrix of order n. If there exists a matrix B of order n such that AB = BA = I, where I is the identity matrix of order n, then the matrix A is said to be invertible and B is called the inverse (or reciprocal) of ..
Note 1:
Only a square matrix can have its invers..
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