Complex Numbers: Argument Traps
Test your handling of the argument of a complex number — the principal interval, the quadrant, and the rules that look as if they should carry over from real numbers but do not.
Fourteen questions cover the principal value interval, why the quadrant matters, the modulus of a product against the argument of a product, the failure of √a·√b = √(ab) for negatives, the triangle inequality and its equality case, De Moivre, and the cube roots of unity.
Includes the one endpoint of the principal interval that can never occur.
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Sample questions3 of 14 shown
Q1
A student reports the principal argument of a complex number as a value lying in [0, 2π). By the standard NCERT/JEE convention, which interval must the principal value of the argument belong to?
Q2
A point representing a non-zero complex number has negative real part. A student computes its argument simply as tan⁻¹(Im/Re), ignoring the quadrant. How does this answer relate to the true argument?
Q3
For two non-zero complex numbers z₁ and z₂, a student doubts whether |z₁z₂| = |z₁||z₂| may need a correction term like the argument does. Which statement is correct?
What This Quiz Covers
- Principal argument in (−π, π]
- Why the quadrant decides the argument
- Modulus of a product against argument of a product
- Why √a·√b = √(ab) fails for negatives
- Triangle inequality and when equality holds
- Cube roots of unity: ω³ = 1 and 1 + ω + ω² = 0
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