Q62.Let a = Im ( 1+z22iz ) to: (1) (−1, 1) (2) [−1, 1] (3) [0, 1) (4) (−1, 0]
What This Question Tests
The question asks for the range of the imaginary part of a complex expression. By simplifying the expression, the imaginary part `a` can be expressed as `-Re(z)/2 * (1+|z|^2)/|z|^2`. Assuming an implicit condition |z|=1 (common in JEE Main if options are bounded), the expression simplifies to -cosθ, yielding a range of [-1, 1].
Concepts Tested
Formulas Used
Im(Z) = (Z - Z_bar)/(2i)
Re(z) = x
|z|^2 = x^2+y^2
z = r(cosθ + isinθ)
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📋 Question Details
- Chapter
- Complex Numbers
- Topic
- Imaginary part of a complex number
- Year
- 2013
- Shift
- 23 Apr Online
- Q Number
- Q62
- Type
- MCQ
- NCERT Ref
- Class 11 Mathematics Ch 5: Complex Numbers and Quadratic Equations
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