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12th Standard English Medium Maths Subject Complex Numbers Book Back 5 Mark Questions with Solution Part - II

12th Standard

    Reg.No. :
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Maths

Time : 01:00:00 Hrs
Total Marks : 25

    5 Marks

    5 x 5 = 25
  1. Show that \(\left( \frac { 19+9i }{ 5-3i } \right) ^{ 15 }-\left( \frac { 8+i }{ 1+2i } \right) ^{ 15 }\) is purely imaginary.

  2. Let z1, z2 and z3 be complex numbers such that \(\left| { z }_{ 1 } \right\| =\left| { z }_{ 2 } \right| =\left| { z }_{ 3 } \right| =r>0\) and z1+ z2+ z3 \(\neq \) 0 prove that \(\left| \frac { { z }_{ 1 }{ z }_{ 2 }+{ z }_{ 2 }{ z }_{ 3 }+{ z }_{ 3 }{ z }_{ 1 } }{ { z }_{ 1 }+{ z }_{ 2 }+{ z }_{ 3 } } \right| \) = r

  3. If z1, z2, and z3 are three complex numbers such that |z1| = 1, |z2| = 2|z3| = 3 and |z+ z+ z3| = 1, show that |9z1z+ 4z1z+ z2z3| = 6

  4.  If z = x + iy is a complex number such that Im \(\left( \frac { 2z+1 }{ iz+1 } \right) =0\) show that the locus of z is 2x2+ 2y2+ x - 2y = 0

  5. If z = x + iy and arg \(\left( \frac { z-i }{ z+2 } \right) =\frac { \pi }{ 4 } \), then show that x+ y+ 3x - 3y + 2 = 0

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