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AP EAMCET202125 Aug 2021Morning ShiftMathematicsComplex NumberActual

Define f: C R by f(z)=|z|, z C . Then, which of the following is false ?

Options

  1. Af(-z)=f(z), z C
  2. Bf( z )=f(z), z C
  3. Cf (z^2 )=(f(z))^2, z C
  4. Df (z₁^2+z₂^2 )=f (z₁^2 )+f (z₂^2 ), z₁, z₂ C

Correct answer

D. f (z₁^2+z₂^2 )=f (z₁^2 )+f (z₂^2 ), z₁, z₂ C

Step-by-step solution

Given, f(z)=|z| (a) f(-z)=f(z) is true |z|=|-z| (b) f( z )=f(z) is true | z |=|z| (c) aligned & f (z^2 )=[f(z)]^2 is true & |z^n |=|z|^n & f (z^2 )= |z^2 |=|z|^2=[f(z)]^2 aligned (d) aligned & f (z₁^2+z₂^2 )=f (z₁^2 )+f (z₂^2 ) & f (z₁^2+z₂^2 )= |z₁^2+z₂^2 | & f (z₁^2 )+f (z₂^2 )= |z₁^2 |+ |z₂ |^2 & |z₁^2+z₂^2 | |z₁ |^2+ |z₂ |^2 aligned It is false.

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