Q62.A value of θ for which 2+3i sin θ is purely imaginary, is 1−2i sin θ (1) sin−1( √34 ) (2) sin−1( √31 ) (3) π (4) π 3 6
What This Question Tests
This question tests the ability to perform division of complex numbers and identify the condition for a complex number to be purely imaginary (real part equals zero). It then requires solving a trigonometric equation.
Concepts Tested
Formulas Used
(a+bi)/(c+di) = [(ac+bd) + i(bc-ad)] / (c^2+d^2)
sin^2(θ) + cos^2(θ) = 1
📚 NCERT Sections This Tests
9.21 — At What Angle Should A Ray Of Light Be Incident On The Face Of A Prism
Physics Class 12 · Chapter 9
9.21 At what angle should a ray of light be incident on the face of a prism of refracting angle 60° so that it just suffers total internal reflection at the other face? The refractive index of the material of the prism is 1.524.
9.17 — (A) Sin I¢C = 1.44/1.68 Which Gives I¢C = 59°. Total Internal Reflection
Physics Class 12 · Chapter 9
9.17 (a) sin i¢c = 1.44/1.68 which gives i¢c = 59°. Total internal reflection takes place when i > 59° or when r < rmax = 31°. Now, (sin i /sin r max max ) = 1.68 , which gives imax ~ 60°. Thus, all incident rays of angles in the range 0 < i < 60° will suffer total internal reflections in the pipe. (If the length of the pipe is finite, which it is in practice, there will be a lower limit on i determined by the ratio of the diameter to the length of the pipe.) (b) If there is no outer coating, i¢c = sin–1(1/1.68) = 36.5°. Now, i = 90° will have r = 36.5° and i¢ = 53.5° which is greater than i¢c. Thus, all incident rays (in the range 53.5° < i < 90°) will suffer total internal reflections.
5.12 — Write All The Geometrical Isomers Of [Pt(Nh3)(Br)(Cl)(Py)] And How Many Of
Chemistry Class 11 · Chapter 5
5.12 Write all the geometrical isomers of [Pt(NH3)(Br)(Cl)(py)] and how many of these will exhibit optical isomers?
📋 Question Details
- Chapter
- Complex Numbers
- Topic
- Purely imaginary complex numbers
- Year
- 2016
- Shift
- 03 Apr
- Q Number
- Q62
- Type
- MCQ
- NCERT Ref
- Class 11 Mathematics Ch 5: Complex Numbers and Quadratic Equations
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