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NDA 1 2024 Maths, question 2

Topic: Algebra

Q2

If zz is any complex number and iz3+z2−z+i=0iz^{3}+z^{2}-z+i=0, where i=−1i=\sqrt{-1}, then what is the value of (∣z∣+1)2(|z|+1)^{2} ?

  1. (a) 11
  2. (b) 44Correct answer
  3. (c) 8181
  4. (d) 121121

Solution.

Answer: (b) 44

  1. Factor the polynomial as (z−i)(iz²−1)=0.
  2. Thus z=i or z²=−i.
  3. In either case |z|=1: in the second case |z|²=|−i|=1.
  4. Hence (|z|+1)²=4.