MHT CET202519 Apr 2025Morning ShiftMathematicsComplex NumberActual
The modulus of the square root of the conjugate of -7+24 -1 is ....
Options
- A3
- B4
- C16
- 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