Complex Conjugates MCQ

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• If z and ω are the complex conjugates of each other, then find the value of (lnz+lnω)/ln|z|.
  ক

  1

  খ

  2

  গ

  3

  ঘ

  4
• The hyperbola, x2–y2=1 can be represented on the Argand Plane by which of the following equations?
  ক

  z2-z̅2=1

  খ

  z2+z̅2=1

  গ

  z2-z̅2=2

  ঘ

  z2+z̅2=2
• If the complex numbers (x2-3x+2)+i(y2-11y+40) and (x2-6x+8)+i(y2-9x+10) are conjugates of each other, Then what is the value of |x+iy|?
  ক

  131/2

  খ

  191/2

  গ

  231/2

  ঘ

  291/2
• If a complex number z, with integral real and imaginary parts, satisfies z2+ z̅2=16, then find the value of |z|.
  ক

  21/2

  খ

  4

  গ

  81/2

  ঘ

  101/2
• Let z=sinx+icos2x and ω=cosx-isin2x. Then for what values of x are z and ω conjugate of each other?
  ক

  x = nπ

  খ

  x = 0

  গ

  x = (n+1/2)π

  ঘ

  no value of x
• For a complex number z, if Re(z) and Im(z) are the roots of x2-7x+12=0 and z+z̅ is one of the roots of x2–10x+16=0, then, find Re(z)-Im(z).
  ক

  1

  খ

  -1

  গ

  3

  ঘ

  -3
• Consider the complex number z, for which a line segment A is drawn connecting origin and the point z. Also, consider the line segment B connecting origin and z̅. if z = x+iy, and the smaller angle between A and B is α, then select the incorrect option.
  ক

  α=π/2 if x=y

  খ

  α>π/2 if |y|>|x|

  গ

  α=π/2 if x=-y

  ঘ

  α=2×Arg(z)
• What is the area of the rectangle whose vertices are the roots of the equation zz̅3+z̅z3=350, given that Re(z) and Im(z) are integers ?
  ক

  12

  খ

  24

  গ

  36

  ঘ

  48
• For two complex numbers p and q, if Arg(p)-Arg(q)=π/2 as well as |pq|=1, what is the value of p̅q ?
  ক

  -i

  খ

  -1

  গ

  i

  ঘ

  1
• Consider two complex numbers, x and y satisfying |x|=|y| and Arg(x)+Arg(y)=π. What is x in terms of y?
  ক

  y̅

  খ

  -y̅

  গ

  y

  ঘ

  -y