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JEE Main201910 Jan 2019Evening ShiftMathematicsComplex NumberActual

Let z = 3 2 + i 2 5 + 3 2 - i 2 5 . If R z and I z respectively denote the real and imaginary parts of z , then

Options

  1. AI z = 0
  2. BR z < 0 and I z > 0
  3. CR z > 0 and I z > 0
  4. DR z = - 3

Correct answer

A. I z = 0

Step-by-step solution

Let &#945; = 3 2 + i 2 , then z = &#945; 5 + &#945; &#175; 5 &#160; We know z &#175; n = z &#175; n &#160; , then, z = 2 R e &#945; 5 &#160; Hence, I z = 0 .

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