number theory problems

If Z = a + ib, then Z is called the negative of Z. -Z = -(a + ib) = -a - ..

Let Z 1 = a + ib and Z 2 = c + id, then ..

If z = x + iy We hav..

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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. Through De Moivre's t..

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 part along the y-axis. This representation of a complex number in..

If Z 1 = a + ib and Z 2 = c + id are two complex numbers, then quotient is defined as ..

Let a=first term, d = common difference, l=t n =last term, s = required sum. Then, Writing the series in the reverse order, Adding together the two series, ..

The total number of all possible subsets of a given set containing n elements is 2 ..

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..