Q62.The set of all α ∈R, for which w = 1+(1−8α)z1−z is a purely imaginary number, for all and Re z ≠1 , is (1) {0} (2) an empty set (3) {0, 14 , −14 } (4) equal to R
What This Question Tests
This question tests the understanding of purely imaginary numbers, requiring the real part of the given complex expression to be zero for any z satisfying |z|=1 and Re(z)≠1.
Concepts Tested
Formulas Used
w is purely imaginary if Re(w) = 0
|z| = 1 implies z * z̄ = 1
📚 NCERT Sections This Tests
14.2 — Which Of The Statements Given In Exercise 14.1 Is True For P-Type
Physics Class 12 · Chapter 14
14.2 Which of the statements given in Exercise 14.1 is true for p-type semiconductos.
8.17 — Complete Each Synthesis By Giving Missing Starting Material, Reagent Or Products
Chemistry Class 12 · Chapter 8
8.17 Complete each synthesis by giving missing starting material, reagent or products
9.15 — Apply Mirror Equation And The Condition:
Physics Class 12 · Chapter 9
9.15 Apply mirror equation and the condition: (a) f < 0 (concave mirror); u < 0 (object on left) (b) f > 0; u < 0 (c) f > 0 (convex mirror) and u < 0 (d) f < 0 (concave mirror); f < u < 0 to deduce the desired result.
📋 Question Details
- Chapter
- Complex Numbers
- Topic
- Properties of complex numbers
- Year
- 2018
- Shift
- 15 Apr Shift 1 Online
- Q Number
- Q62
- Type
- MCQ
- NCERT Ref
- Class 11 Mathematics Ch 5: Complex Numbers
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