Q62.The complex number z = πi−1 π is equal to: cos 3 +i sin 3 (1) √2i(cos 5π12 −i sin 5π12 ) (2) cos 12π −i sin 12π (3) √2(cos 12π + i sin 12π ) (4) √2(cos 5π12 + i sin 5π12 )
What This Question Tests
The question requires converting a complex number from Euler's form to a standard polar form, involving finding the modulus and argument by using standard trigonometric identities and angle manipulation.
Concepts Tested
Formulas Used
e^(iθ) = cosθ + i sinθ
z = r(cosθ + i sinθ)
cos(A+B)
sin(A+B)
📚 NCERT Sections This Tests
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📋 Question Details
- Chapter
- Complex Numbers
- Topic
- Euler form and polar form of complex numbers
- Year
- 2023
- Shift
- 31 Jan Shift 2
- Q Number
- Q62
- Type
- MCQ
- NCERT Ref
- Class 11 Mathematics Ch 5: Complex Numbers and Quadratic Equations
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