Все публикации

0:07:06

Prove that |1+z1*conj(z2)|^2 + |z1-conj(z2)|^2 = [1+|z1|^2][1+|z2|^2].

0:06:06

Find the equation of circle whose radius and center are r and z0 respectively.

0:03:41

Prove that |1/z - 0.5| is less than 0.5 where Re(z) is greater than 1.

0:01:47

Sum to n terms: 1/(1.2) + 1/(2.3) + 1/(3.4) + ...

0:01:16

If A, B are imaginary cube roots of unity show that A^4 + B^4 + 1/(AB) = 0.

0:02:05

Sum to n terms: 1.n + 2(n-1) + 3(n-2) + ...

0:02:15

Find the sum to n terms: (1^2).2 + (2^2).3 + (3^2).4 + ...

0:02:57

Sum to n terms: 2.1 + 5.3 + 8.5 + ...

0:02:20

Find the sum to n terms: 1^2 + 3^2 + 5^2 + ...

0:11:18

Find equations of diagonals of square with a side at angle A to X axis and its end at origin.

0:07:56

Find the diagonals of the parallelogram formed by the given four straight lines.

0:06:47

Find the product of perpendiculars from point (x',y') on the lines a*x^2 + 2hxy + b*y^2 = 0.

0:09:25

Find the square of the distance of the point of intersection of the two given lines from the origin.

0:06:59

Transform the equation 17x^2-16xy+17y^2=225 to axes inclined at 45 degrees to original axes.

0:04:08

Find roots of z^n=(z+1)^n and show that points which represent them are collinear.

0:03:32

Find the area of the triangle whose vertices are the complex numbers 0, z and z*exp(iA).

0:04:02

Find the number of ordered pairs (a,b) such that (a+ib)^2002 = a-ib.

0:02:18

Find all real m such that cube(z)+(3+i)*square(z)-3z-(m+i)=0 has atleast one real root.

0:02:49

Compute z^n + 1/z^n when z+1/z = sqrt(3).

0:04:48

Solve z^4 = 5(z-1)[square(z)-z+1].

0:03:17

Find all quadratic equations one of whose roots is i^51+2i^80+3i^45+4i^38 where i=sqrt(-1).

0:01:46

Find all quadratic equations with real coefficients one of whose roots is (2+i)(3-i).

0:03:33

Factorize cube(x) - 27 into linear polynomials.

0:04:13

Factorize x^4 + 16 into linear polynomials.