Complex Numbers questions
967 published questions with worked solutions.
- What is the value of [ i+ 3 2 ]^ 2019 + [ i- 3 2 ]^ 2019 ?
- If and are the roots of x^2+x+1=0, then what is _ j=0 ^ 3 ( ^j+ ^j ) equal to?
- What is the argument of the complex number 1-i 3 1+i 3 , where i= -1 ?
- What is the modulus of the complex number +i -i , where i= -1 ?
- What is the principal argument of 1 1+i where i= -1 ?
- What is the modulus of ( -3 2 - 1 2 )^ 200 ?
- If is a non-real cube root of 1, then what is the value of | 1- + ^2 |?
- If and are the distinct roots of equation x^2-x+1=0, then what is the value of | ^ 100 + ^ 100 ^ 100 - ^ 100 |?
- If z= 1+i 3 1-i 3 where i= -1 , then what is the argument of z?
- If z is a complex number such that z-1 z+1 is purely imaginary, then what is |z| equal to?
- If z z=|z+ z|, where z=x+iy, i= -1 , then the locus of z is a pair of :
- What is the value of 12+5i + 12-5i , where i= -1 ?
- Which one of the following is a square root of - -1 ?
- If z is any complex number and iz^3+z^2-z+i=0, where i= -1 , then what is the value of (|z|+1)^2?
- If x, y and z are the cube roots of unity, then what is the value of xy+yz+zx?
- Let z_1 and z_2 be two complex numbers such that | z_1+z_2 z_1-z_2 |=1, then what is Re ( z_1 z_2 )+1 equal to?
- If 1 is a cube root of unity, then what are the solutions of (z-100)^3+1000=0?
- What is (1+i)^4+(1-i)^4 equal to, where i= -1 ?
- If Z= 1 3 vmatrix i&2i&1 2i&3i&2 3&1&3 vmatrix =x+iy; i= -1 then what is modulus of Z equal to?
- What is the value of the sum _ n=1 ^ 20 (i^ n-1 +i^n+i^ n+1 ) where i= -1 ?
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