Complex Numbers questions
967 published questions with worked solutions.
- Given z= q+ir 1+p , then p+iq 1+r = 1+iz 1-iz if
- If is a complex cube root of unity, then for positive integral value of n, the product of ^2 ^3 ^n will be
- Statement 1: If (1-i)=a+ib, where a,b R and i= -1 , then a= 12 (e+ 1e ) 1, b= 12 (e- 1e ) 1 Statement 2: e^ i = +i
- The value of _ k=1 ^6 ( 2 k 7-i 2 k 7 ) is
- If x= ( 1+i 2 ), (where i= -1 ), then the expression 2x^4-2x^2+x+3 equals
- If the points z_1,z_2,z_3 are the vertices of an equilateral triangle in the complex plane, then the value of z_1^2+z_2^2+z_3^2...
- If z^2+z|z|+|z|^2=0, then the locus of z is
- If z_1 and z_2 be complex numbers such that z_1 z_2 and |z_1|=|z_2|. If z_1 has positive real part and z_2 has negative imaginary...
- If ( 1) is a cube root of unity and (1+ )^7=A+B , then A and B are respectively
- If ( +i )( 2 +i 2 ) ( n +i n )=1, then the value of is
- If z_1,z_2,z_3 be three complex numbers such that |z_1+1| 1, |z_2+2| 2 and |z_3+4| 4, then the maximum value of |z_1|+|z_2|+|z_3|...
- The real part of (1- +2i )^ -1 is
- If 1, , ^2 are the cube roots of unity, then = vmatrix 1& ^n& ^ 2n ^n& ^ 2n &1 ^ 2n &1& ^n vmatrix is equal to
- The closest distance of the origin from a curve given as a z+ az+|a|^2=0 is
- Let , be the roots of x^2-2x +1=0, then the equation whose roots are ^n, ^n, is
- Let |z|=2 and w= z+1 z-1 where z,w C (where C is the set of complex numbers). Then product of least and greatest value of modulus...
- If the expression (1+ir)^3 is of the form s(1+i) where real s where r is also real and, then the sum of all possible values of r...
- If x=a+bi is a complex number such that x^2=3+4i and x^3=2+11i where i= -1 , then (a+b) equal to
- If complex number z(z 2) satisfies the equation z^2=4z+|z|^2+ 16 |z|^3 then the value of |z|^4 is
- Let z=9+bi where b is non zero real and i^2=-1. If the imaginary part of z^2 and z^3 are equal, then b/3 is
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