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NDA 1 2025 Maths, question 16

Topic: Algebra

Q16

If z≠0z \neq 0 is a complex number, then what is amp(z)+amp(z‾)amp(z) + amp\left( \overline{z} \right) equal to?

  1. (a) 0Correct answer
  2. (b) π/2\pi/2
  3. (c) π\pi
  4. (d) 2π2\pi

Solution.

Answer: (a) 0

  1. The conjugate z‾\overline{z} is the reflection of zz in the real axis.
  2. So amp(z‾)=−amp(z)amp(\overline{z}) = -amp(z), and the sum is 0.

Trap: For a negative real number such as z=−1z = -1, both principal arguments equal π\pi; the standard answer takes the general case.