alleryStart learning →The conjugate of z = a + ib is:
- a - ib
- -a + ib
- -a - ib
- a + ib
Show answer and solution
Correct answer: A. a - ib
Conjugate z̄ = a - ib (flip the sign of imaginary part).
**Geometrically:** reflection across the real axis in the Argand plane.
Indian Navy AA (Artificer Apprentice) Complex Numbers and Quadratic Equations — practice questions
Explore 5 free Complex Numbers and Quadratic Equations questions in Indian Navy AA (Artificer Apprentice) Mathematics. Open each question or exercise to read its content, reference answers and available explanation.
Practise Complex Numbers and Quadratic Equations with Quill →Complex Numbers and Quadratic Equations questions and exercises with answers
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The conjugate of z = a + ib is:Read the answer and worked solution →For z = 1 + i, find arg(z):Read the answer and worked solution →Convert i to polar form:Read the answer and worked solution →Find roots of z² - 4z + 5 = 0:Read the answer and worked solution →Quadratic discriminant — true or false?Read the answer and worked solution →
Worked practice questions
For z = 1 + i, find arg(z):
- π/2
- π/4
- 0
- π
Show answer and solution
Correct answer: B. π/4
z = 1 + i corresponds to (1, 1) in Argand plane, in first quadrant.
tan θ = 1/1 = 1, so θ = π/4 (45 degrees).
Convert i to polar form:
- 1(cos π/2 + i sin π/2)
- 1(cos 0 + i sin 0)
- i
- 2(cos π/4 + i sin π/4)
Show answer and solution
Correct answer: A. 1(cos π/2 + i sin π/2)
i = 0 + 1i corresponds to (0, 1) in Argand plane.
|i| = 1, arg(i) = π/2. So i = 1(cos π/2 + i sin π/2) = cos π/2 + i sin π/2.
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