Complex Numbers questions
967 published questions with worked solutions.
- If z = x+iy satisfies amp (z-1) = amp (z+3i) then the value of (x-1):y is equal to
- Let z be a complex number of constant modulus such that z^2 is purely imaginary then the number of possible values of z is
- If is a nonreal cube root of unity then the expression (1- )(1- ^2)(1+ ^4)(1+ ^8) is equal to
- If 3^ 49 (x+iy) = ( 32 + 3 2 i )^ 100 and x = ky then k is
- If x^2 - x + 1 = 0 then the value of _ n=1 ^ 5 (x^n + 1 x^n )^2 is
- The smallest positive integral value of n for which (1+ 3 i)^ n/2 is real is
- If i= -1 , = nonreal cube root of unity then (1+i)^ 2n - (1-i)^ 2n (1+ ^4- ^2)(1- ^4+ ^2) is equal to
- If z^2 - z + 1 = 0 then z^n - z^ -n , where n is a multiple of 3, is
- If is a nonreal cube root of unity then 1+2 +3 ^2 2+3 + ^2 + 2+3 + ^2 3+ +2 ^2 is equal to
- If z_r= 2r 5 +i 2r 5 , r=0,1,2,3,4, then z_1z_2z_3z_4z_5 is equal to
- If e^ i = +i then for the ABC, e^ iA e^ iB e^ iC is
- If ( 3+i)^n=( 3-i)^n, n N then the least value of n is
- If the fourth roots of unity are z_1,z_2,z_3,z_4 then z_1^2+z_2^2+z_3^2+z_4^2 is equal to
- If x^3-1=0 has the nonreal complex roots , then the value of (1+2 + )^3-(3+3 +5 )^3 is
- If i= -1 then 4+5 (- 12+i 3 2 )^ 334 -3 ( 12+i 3 2 )^ 365 is equal to
- If ( 3-i)^n=2^n, n Z , the set of integers, then n is a multiple of
- If z(2-i2 3)^2=i( 3+i)^4 then amplitude of z is
- The value of amp (i )+ amp (i ^2), where i= -1 and = [3] 1 = nonreal, is
- If , be two complex numbers then | |^2+| |^2 is equal to
- The set of values of a R for which x^2+i(a-1)x+5=0 will have a pair of conjugate complex roots 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