questionrEarly access

Complex Numbers

Showing 50 of 455 · 455 total
  1. 101.Let S be the set of positive integral values of a for which [a condition on a not preserve…
  2. 102.For 0<c<b<a, let (a+b-2c)x^2+(b+c-2a)x+(c+a-2b)=0 and 1 be one of its roots.
  3. 103.Let a,b,c be the lengths of the three sides of a triangle satisfying the condition (a^2+b^…
  4. 104.Let S=zC: |z-1|=1 and (√2-1)(z+ z)-i(z- z)=2√2.
  5. 105.If z is a complex number such that |z|1, then the minimum value of [an expression in z not…
  6. 106.Let and be the roots of the equation px^2+qx-r=0, where p0.
  7. 107.Let p,q R and (1-√3 i)^200=2^199(p+iq), i=-1.
  8. 108.The value of (1+29+i291+29-i29)^3 is:
  9. 109.Let z_1=2+3i and z_2=3+4i.
  10. 110.Let z be a complex number such that |z-2iz+i|=2, z-i.
  11. 111.For two non-zero complex numbers z_1 and z_2, if Re(z_1z_2)=0 and Re(z_1+z_2)=0, then whic…
  12. 112.Let =8-14i, A=z C: z- zz^2- z^2-112i=1 and B=z C: |z+3i|=4.
  13. 113.Let z=1+i and z_1=1+i zz(1-z)+1z.
  14. 114.For all z C on the curve C_1: |z|=4, let the locus of the point z+1z be the curve C_2.
  15. 115.Let be a root of the equation (a-c)x^2+(b-a)x+(c-b)=0 where a,b,c are distinct real number…
  16. 116.Let R and let the equation E be |x|^2-2|x|+|-3|=0.
  17. 117.The number of real solutions of the equation 3(x+1x)^2-2(x+1x)-1=0, is
  18. 118.Let S=: _2(9^2-4+13)-_2(523^2-4+1)=2.
  19. 119.Let a R and let , be the roots of the equation x^2+60^1/4x+a=0.
  20. 120.Let 0 be a real number.
  21. 121.If the value of a real number a>0 for which x^2-5ax+1=0 and x^2-ax-5=0 have a common real …
  22. 122.The number of real roots of the equation x^2-4x+3+x^2-9=√4x^2-14x+6, is:
  23. 123.The equation e^4x+8e^3x+13e^2x-8e^x+1=0, x R, has:
  24. 124.If the centre and radius of the circle |z-2z-3|=2 are respectively (,) and , then 3(++) is…
  25. 125.Let a,b be two real numbers such that ab<0.
  26. 126.Two dice are thrown independently.
  27. 127.Let S=x R: (√3+√2)^x^2-4+(√3-√2)^x^2-4=10.
  28. 128.Let w_1 be the point obtained by rotating z_1=5+4i about the origin through a right angle …
  29. 129.For a C, let A=z C: Re(a+z)>Im(a+z) and B=z C: Re(a+z)<Im(a+z).
  30. 130.Let C be the circle in the complex plane with centre z_0=12(1+3i) and radius r=1.
  31. 131.Let ,, be the three roots of the equation x^3+bx+c=0.
  32. 132.If a and b are the roots of the equation x^2-7x-1=0, then the value of a^21+b^21+a^17+b^17…
  33. 133.The number of points where the curve f(x)=e^8x-e^6x-3e^4x-e^2x+1, x R cuts the x-axis, is …
  34. 134.Let , be the roots of the equation x^2-√2x+2=0.
  35. 135.Let a,b,c be three distinct positive real numbers such that (2a)^ a=(bc)^ b and b^2=a^ c.
  36. 136.The number of integral solutions x of _x+72(x-72x-3)^20 is:
  37. 137.If the sum of the squares of the reciprocals of the roots and of the equation 3x^2+ x-1=0 …
  38. 138.Let S=z C: |z-3|1, z(4+3i)+ z(4-3i)24.
  39. 139.Let a circle C in the complex plane pass through the points z_1=3+4i, z_2=4+3i, z_3=5i.
  40. 140.Let z_1 and z_2 be two complex numbers such that z_1=-iz_2 and (z_1z_2)=.
  41. 141.Let A=z C: |z+1z-1|<1 and B=z C: (z-1z+1)=23.
  42. 142.If z^2+z+1=0, z C, then _n=1^15|z^n+(-1)^n1z^n|^2 is equal to ____ Answer: 2 *(as recorded…
  43. 143.The area of the polygon, whose vertices are the non-real roots of the equation z=iz^2, is:
  44. 144.The number of points of intersection of |z-(4+3i)|=2 and |z|+|z-4|=6, z C, is
  45. 145.The number of elements in the set z=a+ib C: a,b Z, 1<|z-3+2i|<4 is ____ Answer: 40
  46. 146.Sum of squares of modulus of all the complex numbers z satisfying z+ z=(1+i)z^2 is equal t…
  47. 147.Let and be the roots of the equation x^2+(2i-1)=0.
  48. 148.Let S=z C: |z-2|1, z(1+i)+ z(1-i)2.
  49. 149.Let (z) represent the principal argument of the complex number z.
  50. 150.The sum of all the real roots of the equation (e^2x-4)(6e^2x-5e^x+1)=0 is