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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..

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 = 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..

Graphical representation of Complex numbers - The complex number Z = x + iy may be represented graphically by the point P whose rectangular co-ordinates are (x, y). Thus each point in the plane is associated with a complex number. In the figure, P defines Z = x + iy. I..

The complex number Z = x + iy may be represented graphically by the point P whose rectangular co-ordinates are (x, y). Thus each point in the plane is associated with a complex number. In the figure, P defines Z = x + iy. It is customary to choose x-axis as real axis and y-axi..

Rational and Irrational Numbers..

Question 1 - Question: Show that the sum of the cubes of any number of consecutive integers is divisible by the sum of those integers. Answer: Let the consecutive integers be (n + 1), (n + 2), (n + 3),....,(n + m) Sum of the cubes of integers = S 1 (n+m) and (n+m+1) are consecutive intege..

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

Let Z = a + i b and Z' = x + iy be the additive inverse of Z, then a + x = 0 and b + iy = 0 \ Additive inverse of a + ib is - a - ..