number theory problems

Two complex numbers are equal iff their corresponding real parts and imaginary parts are separately equal..

z = r{cos q +isin q } is called the polar form of the complex number. x + iy (which is in the cartesian form) where 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..

Geometrical representation of a Complex number, Argand diagram - Since every complex number z = x + iy is an order pair of real numbers (x, y), it can therefore be represented by a point P(x,y) in the xy plane by taking the real part along the x-axis and the imaginary ..

If z = x + iy then e z = e (x + iy) = e x e iy ? e z = e x {cos y + i sin y} is called the Exponential form of the Complex number..

Summary - If x and y are any real numbers, then x+iy is called a complex number. In the complex number x+iy, the real numbers x and y are respectively called the real part and imaginary part of x+iy. Two complex numbers are said to be equal if their real..

To find the q th 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 ) ..

Polar form of a Complex number - Let z = x+iy denote the point P(x,y) in the xy plane. Then from the figure, we have z = r{cos q +isin q } is called the polar form of the complex number. x + iy (which is in the cartesian form) whe..

Let z= x + iy be a complex number. Taking log on both side..

Rational and Irrational Numbers..

Properties of Complex numbers - If Z, Z 1 and Z 2 are complex numbers, th..