alleryThe imaginary unit i is defined as:
- √(-1)
- √1
- 1/i
- -1
Show answer and solution
Correct answer: A. √(-1)
i = √(-1) by definition.
**So i² = -1. This is the foundation of complex numbers, allowing extension beyond real numbers.**
JEE Advanced Complex Numbers and Quadratic Equations — practice questions
Explore 40 free Complex Numbers and Quadratic Equations questions in JEE Advanced Mathematics. Open each question or exercise to read its content, reference answers and available explanation.
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The imaginary unit i is defined as:Read the answer and worked solution →For z = 3 + 4i, find |z|:Read the answer and worked solution →The conjugate of z = a + ib is:Read the answer and worked solution →i² + i³ equals:Read the answer and worked solution →In polar form z = r(cos θ + i sin θ), r is called the ___ and θ is the ___:Read the answer and worked solution →For z = a + ib, Re(z) and Im(z) are:Read the answer and worked solution →Compute (2 + i)(3 - 2i):Read the answer and worked solution →Find (1 + i)²:Read the answer and worked solution →Solve z² + 1 = 0:Read the answer and worked solution →Modulus of z1 z2 where z1 and z2 are complex:Read the answer and worked solution →Argument of z1 z2:Read the answer and worked solution →For z = 1 + i, find arg(z):Read the answer and worked solution →Find z̄ × z (where z = a + ib):Read the answer and worked solution →Convert i to polar form:Read the answer and worked solution →DeMoivre's theorem: (cos θ + i sin θ)ⁿ equals:Read the answer and worked solution →Compute (1 + i)⁸:Read the answer and worked solution →Cube roots of unity are 1, ω, ω². Find 1 + ω + ω²:Read the answer and worked solution →Find n-th roots of unity. For z = 1: how many distinct nth roots in complex plane?Read the answer and worked solution →Find roots of z² - 4z + 5 = 0:Read the answer and worked solution →If z and z̄ are roots of a quadratic with real coefficients, then sum z + z̄ equals:Read the answer and worked solution →Locus of z satisfying |z - 1| = |z - i|:Read the answer and worked solution →The value of i⁴ⁿ⁺³ (n a positive integer) isRead the answer and worked solution →The modulus of the complex number 3 + 4i isRead the answer and worked solution →The conjugate of (2 − 3i) isRead the answer and worked solution →If z = 1 + i, then z² equalsRead the answer and worked solution →The argument (principal value) of the complex number i isRead the answer and worked solution →The multiplicative inverse of (3 + 4i) isRead the answer and worked solution →For complex numbers, which relation is NOT defined?Read the answer and worked solution →The roots of x² + 1 = 0 areRead the answer and worked solution →If z = a + ib is purely imaginary, thenRead the answer and worked solution →
Worked practice questions
For z = 3 + 4i, find |z|:
- 5
- 7
- 3
- 4
Show answer and solution
Correct answer: A. 5
|z| = √(a² + b²) = √(9 + 16) = √25 = 5. The modulus is the distance from origin in the Argand plane.
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.
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