JEE Main Math · U2
Complex Numbers and Quadratic Equations
JEE Main level practice on complex algebra, Argand geometry, roots of unity, quadratic parameters, and complex-root Vieta reasoning.
Test yourself
A focused, distraction-free run through 50 multiple-choice questions. Hints if you need them; your score at the end.
Difficulty guide
The label describes the problem, not your ability.
1/5 - Foundational
Warm-up setup; checks one basic idea.
2/5 - Routine exam skill
Normal syllabus skill; usually one main rule or interpretation.
3/5 - Standard multi-step
Exam-style problem with multiple steps or a common trap.
4/5 - Hard exam skill
High-end exam problem; combines methods carefully.
5/5 - Challenge
Stretch problem beyond normal exam pressure.
Topic 2.1
Complex Algebra, Conjugates, and Modulus
Algebraic manipulation, conjugate traps, modulus conditions, and Cartesian form.
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Topic 2.2
Argand Plane, Argument, Polar Form, and Loci
Argument constraints, polar conversion, and geometric loci in the complex plane.
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Topic 2.3
Roots of Unity and De Moivre Powers
Cyclic powers, roots of unity, equations in complex roots, and symmetric sums.
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Topic 2.4
Quadratic Equations, Nature of Roots, and Parameters
Discriminant reasoning, parameter ranges, common roots, and integer-root constraints.
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Topic 2.5
Mixed Complex-Quadratic Reasoning
Complex roots of quadratics, transformed roots, conjugate pairs, and mixed Vieta problems.
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