Mathematics questions
18011 published questions with worked solutions.
- If (a_1+ib_1)(a_2+ib_2) (a_n+ib_n)=A+iB, then _ i=1 ^n ^ -1 ( b_i a_i ) is equal to
- If z_1,z_2,z_3, ,z_n are nth roots of unity, then for k=1,2, ,n
- If z_1,z_2 are two complex numbers such that Im (z_1+z_2)=0, Im (z_1z_2)=0, then
- If z_1,z_2 are two complex numbers such that | z_1-z_2 z_1+z_2 |=1 and iz_1=kz_2 where k R, then the angle between z_1-z_2 and...
- The expression i ( a-ib a+ib ) reduces to
- Let z be a complex number (not lying on x-axis) of maximum modulus such |z+ 1z |=1. Then
- The vector z=-4+5i is turned counterclockwise through an angle of 180^ and stretched 1 12 times. The complex number corresponding...
- If z is a complex number, then |z-3-4i|^2+|z+4+2i|^2=k represents a circle, if k is equal to
- If |z_1|=|z_2|=|z_3|=1 and z_1,z_2,z_3 represent the vertices of an equilateral triangle, then
- Let a R. If the origin and the non-real roots of 2z^2+2z+a=0 form the three vertices of an equilateral triangle in the argand...
- If a complex number z lies in the interior or on the boundary of a circle of radius 3 and centre at (-4,0), then the greatest and...
- The joint of z_1=a+ib and z_2= 1 -a+ib passes through
- If z is a complex number in the Argand plane such that ( z-3 3 z+3 3 )= 3, then the locus of z is
- If is a complex cube root of unity, then (1- + ^2 )^6+ (1- ^2+ )^6=
- If is a complex cube root of unity, then the equation |z- |^2+ |z- ^2 |^2= will represent a circle, if
- If a>0 and the equation |z-a^2 |+|z-2a|=3 represents an ellipse, then a belongs to the interval
- If z_r (r=0,1,2, ,6) be the roots of the equation (z+1)^7+z^7=0, then _ r=0 ^6 Re (z_r )=
- If z=i (2- 3 ), then z=
- The general value of which satisfies the equation ( +i )( 3 +i 3 )( 5 +i 5 ) ( (2n-1) +i (2n-1) )=1 is
- If x_n= 3^n +i 3^n , then x_1 x_2 x_3 x_ is equal to