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Most Important Selected Qs for JEE AdvancedMathematicsComplex Number

A complex number z is rotated in anticlockwise direction by an angle and we get z^ and if the same complex number z is rotated by an angle in clockwise direction and we get z^ then

Options

  1. Az^ , z, z^ are in G.P.
  2. Bz^ 2 +z^ 2 =2 z^2 2
  3. Cz^ +z^ =2 z
  4. Dz^ , z, z^ are in H.P.

Correct answer

C. z^ +z^ =2 z

Step-by-step solution

aligned & z^ =z e^ i ....(1) & z^ =z e^ -i ....(2) & z^ z^ =z^2 z^ , z, z^ are in G.P. & ( z^ z )^2+ ( z^ z )^2=2 2 & z^ 2 +z^ 2 =2 z^2 2 & z^ +z^ =2 z aligned

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