Q52.If z1, z2 are complex numbers such that Re (z1) = |z1 −1| and Re (z2) = |z2 −1| and arg(z1 −z2) = π6 , then Im(z1 + z2) is equal to : (1) 2√3 (2) √3 2 (3) 1 (4) 2 √3 √3
What This Question Tests
This problem combines the geometric interpretation of complex numbers to find the locus of points (a parabola) with the argument of the difference between two complex numbers to determine the imaginary part of their sum.
Concepts Tested
Formulas Used
z = x + iy
|z| = √(x² + y²)
arg(z) = tan⁻¹(y/x)
📚 NCERT Sections This Tests
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2.1 — Two Charges 5 × 10–8 C And –3 × 10–8 C Are Located 16 Cm Apart. At
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2.1 Two charges 5 × 10–8 C and –3 × 10–8 C are located 16 cm apart. At what point(s) on the line joining the two charges is the electric potential zero? Take the potential at infinity to be zero.
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📋 Question Details
- Chapter
- Complex Numbers
- Topic
- Geometric Interpretation of Complex Numbers
- Year
- 2020
- Shift
- 03 Sep Shift 2
- Q Number
- Q52
- Type
- MCQ
- NCERT Ref
- Class 11 Mathematics Ch 5: Complex Numbers and Quadratic Equations
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