definition of real numbers

If Z = a + ib is a complex number, then a - ib is called the complex conjugate of a + ib and the conjugate is denoted by..

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..

To find the logarithm of a Complex number - Let z= x + iy be a complex number. Taking log on both side..

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..

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..

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 - ..

Let Z = a + i b and Z' = x + iy, then ax - by = a ..... (i) and ay + bx = b ..... (ii) Solving (i) and (ii), we have x = 1, y =0 Multiplicative identity is 1 + ..