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NDA 2024
Exam
NDA
Year
2024
Subject
Mathematics
Chapter
Complex Number

NDA 2024 · Mathematics · Complex Number

Paragraph: Let Z_1 and Z_2 be any two complex numbers such that...

Paragraph: Let Z1andZ2Z_1 and Z_2 be any two complex numbers such that Z12+Z22+Z1Z2=0Z_1^2+Z_2^2+Z_1 Z_2=0
Question: What is the value of ∣Z1Z2∣\left|\frac{Z_1}{Z_2}\right| ?

Options

  1. A−1-1
  2. B22
  3. C33
  4. D44

Correct answer

A. −1-1

Step-by-step solution

Given that, Z12+Z22+Z1Z2=0⇒Z1=w and Z2=w2∣Z1Z2∣=∣ωω2∣=∣1ω∣=1Z_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
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