Q62.If z z α (α ∈R) is a purely imaginary number and |z| = 2, then a value of α is : + (1) 1 (2) 12 (3) √2 (4) 2
What This Question Tests
The question asks for a value of real α such that the expression `z + α/z` is purely imaginary for |z|=2. By setting the real part of the expression to zero, we find two conditions: either Re(z)=0 or α=-4. Since α=-4 is not an option, we consider the case Re(z)=0. If Re(z)=0, then z is purely imaginary, i.e., z = ±2i. For such a z, the expression `z + α/z` becomes `±2i + α/(±2i) = ±2i - iα/2 = i(±(2-α/2))`, which is always purely imaginary for any real α. As the question asks for 'a value', and `α=1` is an option, it serves as a valid answer.
Concepts Tested
Formulas Used
z = x + iy
|z|^2 = x^2 + y^2
Re(z) = x
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📋 Question Details
- Chapter
- Complex Numbers
- Topic
- Properties of Complex Numbers
- Year
- 2019
- Shift
- 12 Jan Shift 1
- Q Number
- Q62
- Type
- MCQ
- NCERT Ref
- Class 11 Mathematics Ch 5: Complex Numbers and Quadratic Equations
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