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NDA2021MathematicsComplex NumberActual

Consider the following statements in respect of an arbitrary complex number Z : 1. The difference of Z and its conjugate is an imaginary number. 2. The sum of Z and its conjugate is a real number. Which of the above statements is/are correct?

Options

  1. A1 only
  2. B2 only
  3. CBoth 1 and 2
  4. DNeither 1 nor 2

Correct answer

C. Both 1 and 2

Step-by-step solution

Let z=x+i y conjugate of z^ =x-i y Now, z+z^ =x+i y+x-i y=2 x (Real) z-z^ =x+i y-x+i y=(2 y) i (Imaginery) Hence, both (1) and (2) are true.

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