Q61.If z ≠1 and z−1z2 is real, then the point represented by the complex number (1) either on the real axis or on a circle passing (2) on a circle with centre at the origin through the origin (3) either on the real axis or on a circle not passing (4) on the imaginary axis through the origin
What This Question Tests
This question requires using the property that a complex number is real if it is equal to its conjugate, and then algebraically manipulating the expression to determine the locus of the complex number z.
Concepts Tested
Formulas Used
w is real iff w = w̄
z = x + iy
z̄ = x - iy
z z̄ = |z|^2
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📋 Question Details
- Chapter
- Complex Numbers
- Topic
- Locus of a complex number
- Year
- 2012
- Shift
- Offline
- Q Number
- Q61
- Type
- MCQ
- NCERT Ref
- Class 11 Mathematics Ch 5: Complex Numbers and Quadratic Equations
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