Q63.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) {0, 14 , −14 } (3) equal to R (4) an empty set
What This Question Tests
This problem tests a deep understanding of complex numbers, specifically the condition for a number to be purely imaginary and the properties of complex numbers on the unit circle, requiring careful algebraic manipulation.
Concepts Tested
Formulas Used
w is purely imaginary ⇒ Re(w) = 0
If |z|=1, then z* = 1/z
📚 NCERT Sections This Tests
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.
14.2 — Which Of The Statements Given In Exercise 14.1 Is True For P-Type
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14.2 Which of the statements given in Exercise 14.1 is true for p-type semiconductos.
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8.17 Complete each synthesis by giving missing starting material, reagent or products
📋 Question Details
- Chapter
- Complex Numbers
- Topic
- Purely imaginary numbers, properties of modulus
- Year
- 2018
- Shift
- 15 Apr
- Q Number
- Q63
- Type
- MCQ
- NCERT Ref
- Class 11 Mathematics Ch 5: Complex Numbers and Quadratic Equations
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