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MHT CET202519 Apr 2025Morning ShiftMathematicsComplex NumberActual

The modulus of the square root of the conjugate of -7+24 -1 is ....

Options

  1. A3
  2. B4
  3. C16
  4. D5

Correct answer

D. 5

Step-by-step solution

The complex number is z = -7 + 24i , so its conjugate is z = -7 - 24i . The modulus of z is calculated as | z | = (-7)^2 + (-24)^2 = 49 + 576 = 625 = 25 . Using the property | w | = |w| for any complex w , we find | z | = | z | = 25 = 5 . Alternatively, solving -7 - 24i = x + iy leads to (z = 3 - 4i) or (z = -3 + 4i) , both of which have modulus 5 . Final answer: 5

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