Complex Numbers questions
967 published questions with worked solutions.
- If 1, , ^2 are the cube roots of unity, then vmatrix 1+ & ^2&- 1+ ^2& &- ^2 ^2+ & &- ^2 vmatrix =
- If a+b+c 0, then (a+b +c ^2)^3+(a+b ^2+c )^3=
- If a= 2i , then which of the following is correct?
- The locus of the point z satisfying ( z-1 z+1 )=k, where k is non-zero real, is
- If |z_1|=|z_2|=|z_3| and z_1+z_2+z_3=0, then z_1,z_2,z_3 are vertices of
- 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
- 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
Other chapters
Alcohols, Phenols and EthersAldehydes, Ketones and Carboxylic AcidsAlternating CurrentAminesAnatomy of Flowering PlantsAncient Indian HistoryAnimal KingdomApplication of DerivativesArea Under CurveAromatic Compounds and Aryl HalidesAtomsBasic Mathematics and LogarithmBinomial TheoremBiodiversity and ConservationBiological ClassificationBiomoleculesBiotechnology and Its ApplicationsBiotechnology: Principles and ProcessesBody Fluids and CirculationBreathing and Exchange of GasesCell Cycle and Cell DivisionCell: The Unit of LifeChemical Bonding and Molecular StructureChemical Coordination and Integration