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Indian Navy SSR (Sailor) Complex Numbers and Quadratic Equations — practice questions

Explore 5 free Complex Numbers and Quadratic Equations questions in Indian Navy SSR (Sailor) Mathematics. Open each question or exercise to read its content, reference answers and available explanation.

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Complex Numbers and Quadratic Equations questions and exercises with answers

Showing questions 1–5 of 5.

Find z̄ × z (where z = a + ib):Read the answer and worked solution →If z = 1 + i, then z² equalsRead the answer and worked solution →The value of $i + i^2 + i^3 + i^4$ is:Read the answer and worked solution →Real or imaginary?Read the answer and worked solution →Which one does NOT belong?Read the answer and worked solution →

Worked practice questions

Find z̄ × z (where z = a + ib):

  1. a² + b² = |z|²
  2. 2a
  3. a² - b²
  4. |z|
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Correct answer: A. a² + b² = |z|²

We have z × z̄ = (a + ib)(a - ib). That is z × z̄ = a² - (ib)². That is z × z̄ = a² + b². So z × z̄ = |z|². **So conjugate times itself gives modulus squared.**

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If z = 1 + i, then z² equals

  1. 2
  2. 1 + 2i
  3. −2i
  4. 2i
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Correct answer: D. 2i

We have (1+i)² = 1 + 2i + i². That is (1+i)² = 1 + 2i − 1. So (1+i)² = 2i.

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The value of $i + i^2 + i^3 + i^4$ is:

  1. 0
  2. $1$
  3. $-1$
  4. $i$
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Correct answer: A. 0

We have i + i² + i³ + i⁴ = i − 1 − i + 1. So i + i² + i³ + i⁴ = 0.

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