Mathematics questions
18011 published questions with worked solutions.
- The equation bz+b z=c, where b is a non-zero complex constant and c is a real number, represents
- If P,P' represent the complex number z_1 and its additive inverse respectively, then the equation of the circle with PP' as a...
- If z_0= 1-i 2, then the value of the product (1+z_0) (1+z_0^2 ) (1+z_0^ 2^2 ) (1+z_0^ 2^3 ) (1+z_0^ 2^n ) must be
- If , , are the cube roots of p, p<0 then for any x,y and z the values of x +y +z x +y +z are
- Number of solutions of the equation z^2+|z|^2=0, where z C is
- Let z( 2) be a complex number such that _ 1/2 |z-2|> _ 1/2 |z|, then
- Find the complex number z satisfying the equations | z-12 z-8i |= 53, | z-4 z-8 |=1
- If 1, , ^2, , ^ n-1 are the n, n^ th roots of unity and z_1 and z_2 are any two complex numbers, then _ r=0 ^ n-1 |z_1+ ^rz_2 |^2=
- If z_n= n(n+1)(n+2) +i n(n+1)(n+2) for n=1,2,3, , then the valu of (z_1z_2 z_n) is
- If |z-25i| 15, then | maximum amp (z)- minimum amp (z)|=
- The area of the triangle formed by the points representing -z, iz and z-iz in the Argand plane is
- If vmatrix 6i&-3i&1 4&3i&-1 20&3&i vmatrix =x+iy, then
- If |z-4-3i| 1 and m and n are the least and greatest value of |z| and is the least value of x^4+x^2+4 x in the interval (0, )...
- If is an imaginary cube root of unity, then the value of ( ^ 10 + ^ 23 ) - 4 is
- The locus of the centre of the circle which touches the circles |z-z_1|=a and |z-z_2|=b externally (z, z_1 and z_2 are complex...
- Let be a complex cube root of unity. If the equation |z- |^2+ |z- ^2 |^2= represents a circle with points representing and ^2 as...
- The system of equation |z+1-i|= 2 and |z|=3 has
- If z+z^ -1 =1, then z^ 100 +z^ -100 is equal to
- (1+i)^8+(1-i)^8=
- If the complex numbers z_1=a+i, z_2=1+ib, z_3=0 form the vertices of equilateral triangle (a,b are real numbers between 0 and 1),...