Q41 / 120 · NDA 2024 (Phase 2) · Mathematics

Paragraph: Let $Z_1$ and $Z_2$ be any two complex numbers such that $Z_1^2+Z_2^2+Z_1 Z_2=0$
Question: What is the value of $\left|\frac{Z_1}{Z_2}\right|$ ?

  • Correct answer
    A
    $-1$
  • B
    $2$
  • C
    $3$
  • D
    $4$

Solution

Given that, $Z_1^2+Z_2^2+Z_1 Z_2=0 \Rightarrow Z_1=w \text { and } Z_2=w^2$ $\left|\frac{Z_1}{Z_2}\right|=\left|\frac{\omega}{\omega^2}\right|=\left|\frac{1}{\omega}\right|=1$

Hence, the correct answer is option: 'A'.

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