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Complex Numbers

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  1. 201.Let S_1,S_2,S_3 be S_1=z C:|z-1|√2, S_2=z C:Re[(1-i)z]1, S_3=z C:Im(z)1.
  2. 202.The area of the triangle with vertices A(z), B(iz), C(z+iz) is
  3. 203.The value of 4+15+14+15+14+ is
  4. 204.Let P(x)=x^2+bx+c be a quadratic polynomial with real coefficients, such that _0^1P(x),dx=…
  5. 205.Let z and w be two complex numbers, such that w=z z-2z+2, |z+iz-3i|=1 and Re(w) has minimu…
  6. 206.The least value of |z|, where z is a complex number satisfying ![(|z|+3)(|z|-1)|z|+12]_√2!…
  7. 207.If f(x) and g(x) are two polynomials such that the polynomial P(x)=f(x^3)+xg(x^3) is divis…
  8. 208.The value of 3+14+13+14+13+ is equal to
  9. 209.Let C be the set of all complex numbers.
  10. 210.The point P(a,b) undergoes reflection about y=x, then translation 2 units along positive X…
  11. 211.Let C be the set of complex numbers.
  12. 212.Let , be two roots of the equation x^2+(20)^1/4x+(5)^1/2=0.
  13. 213.The number of real roots of the equation e^4x-e^3x-4e^2x-e^x+1=0 is equal to Answer: 2
  14. 214.The number of real roots of the equation e^6x-e^4x-2e^3x-12e^2x+e^x+1=0 is
  15. 215.If , are roots of x^2+5√2x+10=0, >, and P_n=^n-^n for each positive integer n, then the va…
  16. 216.The number of real solutions of the equation x^2-|x|-12=0 is
  17. 217.Let [x] denote the greatest integer less than or equal to x.
  18. 218.If and are the distinct roots of x^2+3^1/4x+3^1/2=0, then the value of ^96(^12-1)+^96(^12-…
  19. 219.If the real part of z=3+2i1-3i, [0,2], is zero, then ^23+^2 is equal to Answer: 1
  20. 220.Let n denote the number of solutions of the equation z^2+3 z=0, where z is a complex numbe…
  21. 221.If the real part of (1-+2i)^-1 is 15 for (0,), then the value of _0^ x,dx is equal to
  22. 222.If z and are two complex numbers such that |z|=1 and (z)-()=32, then !(1-2z1+3z) is
  23. 223.Let Z_1 and Z_2 be two complex numbers such that (Z_1-Z_2)=4, and Z_1,Z_2 satisfy |Z-3|=Re…
  24. 224.The number of distinct real roots of the equation 3x^4+4x^3-12x^2+4=0 is Answer: 4
  25. 225.The set of all values of k>-1, for which the equation (3x^2+4x+3)^2-(k+1)(3x^2+4x+3)(3x^2+…
  26. 226.The sum of all integral values of k (k0) for which the equation 2x-1-1x-2=2k in x has no r…
  27. 227.If (√3+i)^100=2^99(p+iq), then p and q are roots of the equation
  28. 228.Let 0 be in R.
  29. 229.If S=z C:z-iz+2i R, then
  30. 230.Let z=1-i√32 and i=-1.
  31. 231.The equation !(z-1z+1)=4 represents a circle with
  32. 232.A point z moves in the complex plane such that !(z-2z+2)=4; then the minimum value of |z-9…
  33. 233.If z is a complex number such that z-iz-1 is purely imaginary, then the minimum value of |…
  34. 234.The least positive integer n such that (2i)^n(1-i)^n-2, i=-1, is a positive integer, is An…
  35. 235.The number of pairs (a,b) of real numbers such that whenever is a root of x^2+ax+b=0, ^2-2…
  36. 236.If 3+i4-i, [0,2], is a real number, then an argument of +i is:
  37. 237.Let z be a complex number such that |z-iz+2i|=1 and |z|=52.
  38. 238.If z is a complex number satisfying |Re(z)|+|Im(z)|=4, then |z| cannot be:
  39. 239.Let =-1+i√32.
  40. 240.If Re(z-12z+i)=1, where z=x+iy, then the point (x,y) lies on a:
  41. 241.If x is real, the number of real roots of the equation e^4x+e^3x-4e^2x+e^x+1=0 is:
  42. 242.The least positive value of 'a' for which the equation 2x^2+(a-10)x+332=2a has real roots …
  43. 243.If the equation x^2+bx+45=0 (b R) has conjugate complex roots and they satisfy |z+1|=2√10,…
  44. 244.Let and be the roots of x^2-x-1=0.
  45. 245.Let and be two real roots of the equation (k+1)^2x-√2 x=(1-k), where k(-1) and are real nu…
  46. 246.Let a,b R, a0, be such that ax^2-2bx+5=0 has a repeated root , which is also a root of x^2…
  47. 247.If the four complex numbers z,-z,-z-2Re(-z) and z-2Re(z) represent the vertices of a squar…
  48. 248.The value of (-1+i√31-i)^30 is:
  49. 249.If (1+i1-i)^m/2=(1+ii-1)^n/3=1, (n,m N), then the greatest common divisor of the least val…
  50. 250.If Z_1,Z_2 are complex numbers such that Re(Z_1)=|Z_1-1|, Re(Z_2)=|Z_2-1| and (Z_1-Z_2)=6,…