Mathematics questions
18011 published questions with worked solutions.
- If a,b,c and u,v, are complex numbers representing the vertices of two triangles such that c=(1-r)a+rb and =(1-r)u+rv, where r is...
- Let z_1,z_2,z_3 be three vertices of an equilateral triangle circumscribing the circle |z|= 12. If z_1= 12+i 3 2 and z_1,z_2,z_3...
- If p^2-p+1=0, then the value of p^ 3n can be
- If is a complex cube root of unity, then (1+i)^ 2n -(1-i)^ 2n (1+ ^4- ^2 ) (1- ^4+ ^2 ) is equal to
- Let z_1 and z_2 be two complex numbers such that z_1 z_2 + z_2 z_1 =1. Then,
- If z_1 and z_2 are two complex numbers such that | z_1-z_2 1- z_1z_2 |=1, then which one of the following is not true?
- The area of the triangle whose vertices are i, and ^2, where i= -1 and , ^2 are complex cube roots of unity, is
- If ( 3/2+(1/2)i 3/2-(1/2)i )^ 120 =p+iq, then
- If 2z_1-3z_2+z_3=0, then z_1,z_2,z_3 are represented by
- 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