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JEE Main202229 Jul 2022Morning ShiftMathematicsComplex NumberActual

If z = 2 + 3 i , then z 5 + z ¯ 5 is equal to:

Options

  1. A244
  2. B224
  3. C245
  4. D265

Correct answer

A. 244

Step-by-step solution

Given z = 2 + 3 i , So, z 5 + z ¯ 5 = 2 + 3 i 5 + 2 - 3 i 5 Applying binomial expansion we get, = 2 C 0 5 2 5 + C 2 5 2 3 3 i 2 + C 4 5 2 1 3 i 4 = 2 32 + 10 × 8 - 9 + 5 × 2 × 81 = 244

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