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Complex Numbers question

2010 · Shift 1 · Q32
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  5. /2010 · Shift 1 · Q32

Complex Numbers question

2010 · Shift 1 · Q32

JEE AdvancedMathematicsComplex NumbersMultiple correct+4 / −1
Let z1{{z_1}}z1​ and z2{{z_2}}z2​ be two distinct complex number and let z =( 1 - t) z1{{z_1}}z1​ + t z2{{z_2}}z2​ for some real number t with 0 < t < 1. IfArg (w) denote the principal argument of a non-zero complex number w, then
  1. A
    ∣z−z1∣+∣z−z2∣=∣z1−z2∣\left| {z - {z_1}} \right| + \left| {z - {z_2}} \right| = \left| {{z_1} - {z_2}} \right|∣z−z1​∣+∣z−z2​∣=∣z1​−z2​∣
  2. B
    Arg (z−z1)(z - {z_1})(z−z1​) = Arg (z−z2)(z - {z_2})(z−z2​)
  3. C
    ∣z−z1z‾−z‾1z2−z1z‾2−z‾1∣\left| {\begin{matrix} {z - {z_1}} & {\overline z - {{\overline z }_1}} \\ {{z_2} - {z_1}} & {{{\overline z }_2} - {{\overline z }_1}} \\ \end{matrix} } \right|​z−z1​z2​−z1​​z−z1​z2​−z1​​​ = 0
  4. D
    Arg (z−z1)(z - {z_1})(z−z1​) = Arg (z2−z1)({z_2} - {z_1})(z2​−z1​)
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