Q81.Let z and w be two complex numbers such that w = zz −2z + 2, z−3iz+i = 1 and Re (w) has minimum value. Then, the minimum value of n ∈N for which wn is real, is equal to _______.
What This Question Tests
This question integrates multiple concepts of complex numbers, involving finding the locus of 'z', expressing 'w' in terms of 'z' to minimize its real part, and then using the argument property of complex numbers to find the smallest 'n' for which w^n is real.
Concepts Tested
Formulas Used
|z| = √(x²+y²)
z = x+iy
arg(w^n) = n * arg(w)
w is real if arg(w) = kπ
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📋 Question Details
- Chapter
- Complex Numbers
- Topic
- Locus of complex numbers, modulus, argument, properties of real numbers
- Year
- 2021
- Shift
- 16 Mar Shift 1
- Q Number
- Q81
- Type
- Numerical
- NCERT Ref
- Class 11 Mathematics Ch 5: Complex Numbers and Quadratic Equations
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