Q63.If z is a non-real complex number, then the minimum value of Im z5 is (Where Im z = Imaginary part of z ) (Im z)5 JEE Main 2015 (11 Apr Online) JEE Main Previous Year Paper (1) −2 (2) −4 (3) −5 (4) −1
What This Question Tests
This question requires recognizing that the expression involves `Im(z^5) / (Im(z))^5` (assuming a common typo in PDF extraction). It then necessitates using De Moivre's theorem, a trigonometric identity for `sin 5θ`, and minimizing a quadratic function in terms of `1/sin^2 θ`.
Concepts Tested
Formulas Used
z = r(cos θ + i sin θ)
z^n = r^n(cos nθ + i sin nθ)
Im(z^n) = r^n sin nθ
sin 5θ = 16 sin^5 θ - 20 sin^3 θ + 5 sin θ
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📋 Question Details
- Chapter
- Complex Numbers
- Topic
- Powers of Complex Numbers
- Year
- 2015
- Shift
- 11 Apr Online
- Q Number
- Q63
- Type
- MCQ
- NCERT Ref
- Class 11 Mathematics Ch 5: Complex Numbers
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