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NDA 2 2024 Maths, question 42

Topic: Algebra

Passage · Q41 to Q42

Let Z1Z_{1} and Z2Z_{2} be any two complex numbers such that Z12+Z22+Z1Z2=0Z_{1}^{2}+Z_{2}^{2}+Z_{1}Z_{2}=0.

Q42

What is the value of 12+Re(Z1Z2)\frac{1}{2}+Re\left( \frac{Z_{1}}{Z_{2}} \right)?

  1. (a) −1-1
  2. (b) 00Correct answer
  3. (c) 11
  4. (d) 22

Solution.

Answer: (b) 00

  1. For the defined ratio w=Z₁/Z₂, w²+w+1=0 implies Re(w)=−1/2.
  2. Therefore 1/2+Re(w)=0.
  3. Both conjugate roots give the same value.