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 — practice questions
Explore 5 free Complex Numbers questions in Indian Navy AA (Artificer Apprentice) Mathematics. Open each question or exercise to read its content, reference answers and available explanation.
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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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