Practice questions
88551 published questions with worked solutions.
- Sum of the series _ r=0 ^n(-1)^r , ^nC_r i^ 5r +i^ 6r +i^ 7r +i^ 8r , is
- Let A,B,C be three collinear points such that AB AC=1 and the points are represented in the Argand plane by the complex numbers...
- POQ is a straight line through the origin O. P and Q represent the complex numbers a+ib and c+id respectively and OP=OQ. Then...
- If (a_1+ib_1)(a_2+ib_2) (a_n+ib_n)=A+iB, then (a_1^2+b_1^2 ) (a_2^2+b_2^2 ) (a_n^2+b_n^2 ) is equal to
- If Re (z)<0, then the value of |1+z+z^2+ +z^n | cannot exceed
- The value of _ r=1 ^8 ( 2r 9+i 2r 9 ), is
- If n is a positive integer greater than unity and z is a complex number satisfying the equation z^n=(z+1)^n, then
- If ( 3+i)^ 10 =a+ib, then a and b respectively
- In the argand plane, if O, P and Q represent respectively the origin O and the complex numbers z and z+iz respectively, then OPQ...
- If |z_1|=|z_2| and (z_1)+ (z_2)=0, then
- The complex number satisfying |z+1|=|z-1| and ( z-1 z+1 )= 4 is
- 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