Q63.If z is a complex number of unit modulus and argument θ, then arg ( 1+1+z−z ) can be equal to (1) θ (2) π −θ (3) −θ (4) π2 −θ
What This Question Tests
This question tests the ability to manipulate complex numbers in polar form and find the argument of a complex expression using properties of Euler's formula and half-angle identities. A subtle point regarding the principal argument range is crucial.
Concepts Tested
Formulas Used
z = e^(iθ)
Euler's formula
arg(z1/z2) = arg(z1) - arg(z2)
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📋 Question Details
- Chapter
- Complex Numbers
- Topic
- Argument of complex numbers
- Year
- 2013
- Shift
- 07 Apr
- Q Number
- Q63
- Type
- MCQ
- NCERT Ref
- Class 11 Mathematics Ch 5: Complex Numbers and Quadratic Equations
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