questionrEarly access

Complex Numbers

Showing 50 of 455 · 455 total
  1. 1.The number of values of z C, satisfying the equations |z-(4+8i)|=√10 and |z-(3+5i)|+|z-(5+…
  2. 2.Let S=z C:z^2+√6iz-3=0.
  3. 3.Let the set of all values of k R such that the equation z(z+2+i)+k(2+3i)=0,z C, has at lea…
  4. 4.Let z_1,z_2 C be the distinct solutions of the equation z^2+4z-(1+12i)=0.
  5. 5.Let a,b C.
  6. 6.Let S=z C:z^2+4z+16=0.
  7. 7.Let z be a complex number such that |z+2|=|z-2| and arg ((z+3)/(z-i))=( )/(4).
  8. 8.Let the circles C_1:|z|=r and C_2:|z-3-4i|=5, z C, be such that C_2 lies within C_1.
  9. 9.Let x and y be real numbers such that 50((2x)/(1+3i)-(y)/(1-2i))=31+17i,i=-1.
  10. 10.Let A=z C:|z-2| 4 and B=z C:|z-2|+|z+2|=5.
  11. 11.Let z be a complex number such that |z-6|=5 and |z+2-6 i|=5.
  12. 12.Let S=z C:|(z-6i)/(z-2i)|=1 and |(z-8+2i)/(z+2i)|=(3)/(5).
  13. 13.If z=√32+(i)/(2),i=-1, then (z^201-i)^8 is equal to
  14. 14.Let S=z:3 |2z-3(1+i)| 7 be a set of complex numbers.
  15. 15.Let S=z C:4z^2+z=0.
  16. 16.Let z be the complex number satisfying |z-5| 3 and having maximum positive principal argum…
  17. 17.If x^2+x+1=0, then the value of (x+(1)/(x))^4+(x^2+1x^2)^4+(x^3+1x^3)^4+ +(x^25+1x^25)^4 i…
  18. 18.Let A= [0,2 ]:1+10Re((2 +i )/( -3i ))=0.
  19. 19.If the locus of z C, such that Re((z-1)/(2z+i))+(z-12z-i)=2, is a circle of radius r and c…
  20. 20.Among the statements (S1) : The set z C--i:|z|=1 and (z-i)/(z+i) is purely real contains e…
  21. 21.Let the product of _1=(8+i) +(7+4i) and _2=(1+8i) +(4+7i) be +i , i=-1.
  22. 22.[If,,z_1,z_2,z_3 ,,are,,the,,vertices,,of,,an,,equilateral,,triangle,,,whose,,centroid,,is…
  23. 23.Let z C be such that (z^2+3 i)/(z-2+i)=2+3 i.
  24. 24.Let z be a complex number such that |z|=1.
  25. 25.Let |z_1-8-2i| 1 and |z_2-2+6i| 2, z_1,z_2 C.
  26. 26.If +i and +i are the roots of x^2-(3-2i)x-(2i-2)=0, i=-1, then + is equal to:
  27. 27.Let O be the origin, the point A be z_1=√3+2√2i, the point B(z_2) be such that √3|z_2|=|z_…
  28. 28.If and are the roots of the equation 2z^2-3z-2i=0, where i=-1, then 16 Re( ^19+ ^19+ ^11+ …
  29. 29.The number of complex numbers z, satisfying |z|=1 and |zz+zz|=1, is :
  30. 30.Let |z-i2z+i|=(1)/(3),z C, be the equation of a circle with center at C.
  31. 31.Let the curve z(1+i)+z(1-i)=4,z C, divide the region |z-3| 1 into two parts of areas and .
  32. 32.Let z_1,z_2 and z_3 be three complex numbers on the circle |z|=1 with arg(z_1)=(- )/(4),ar…
  33. 33.Let z be a complex number such that the real part of [(z-2 i)/(z+2 i)] is zero.
  34. 34.The sum of all possible values of [- ,2 ], for which (1+i )/(1-2i ) is purely imaginary, i…
  35. 35.Let z be a complex number such that |z+2|=1 and lm((z+1)/(z+2))=(1)/(5).
  36. 36.If the set R=(a,b):a+5b=42,a,b N has m elements and _n=1^m(1-i^n!)=x+iy, where i=-1, then …
  37. 37.If z_1,z_2 are two distinct complex number such that |z_1-2z_2(1)/(2)-z_1z_2|=2, then
  38. 38.Let S_1=z C:|z| 5,S_2=z C:Im(z+1-√3i1-√3i) 0 and S_3=z C:Re(z) 0.
  39. 39.The area (in sq.
  40. 40.Let and be the sum and the product of all the non-zero solutions of the equation (z)^2+|z|…
  41. 41.If z is a complex number such that |z| 1, then the minimum value of |z+(1)/(2)(3+4i)| is :
  42. 42.Let S=|z C:|z-1|=1 and (√2-1)(z+z)-i(z-z)=2√2|.
  43. 43.Let z_1 and z_2 be two complex numbers such that z_1+z_2=5 and z_3^1+z_3^2=20+15i Then, |z…
  44. 44.If z is a complex number, then the number of common roots of the equations z^1985+z^100+1=…
  45. 45.If z=x+iy,xy 0, satisfies the equation z^2+iz=0, then |z^2| is equal to :
  46. 46.Let r and respectively be the modulus and amplitude of the complex number z=2-i(2 (5 )/(8)…
  47. 47.If z=(1)/(2)-2i is such that |z+1|= z+ (1+i),i=-1 and , R, then + is equal to
  48. 48.If S=z C:|z-i|=|z+i|=|z-1|, then, n(S) is :
  49. 49.If the set Re(z-z+zz2-3z+5z):z C,Re(z)=3 is equal to the interval ( , ], then 24( - ) is e…
  50. 50.Let S=z C:z=i(z^2+Re(z)).