Q82.The least positive integer n such that , i = √−1, is a positive integer, is ______. (1−i)n−2
What This Question Tests
This question requires simplifying a complex expression involving powers of (2i) and (1-i) and determining the least positive integer 'n' for which the result is a positive integer, utilizing properties of 'i' and potentially polar form.
Concepts Tested
Formulas Used
i² = -1, i³ = -i, i⁴ = 1
(1-i) = √2 e^(-iπ/4)
(a+bi)^n
(x+iy) / (a+ib)
📚 NCERT Sections This Tests
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📋 Question Details
- Chapter
- Complex Numbers
- Topic
- Powers of complex numbers
- Year
- 2021
- Shift
- 26 Aug Shift 2
- Q Number
- Q82
- Type
- Numerical
- NCERT Ref
- Class 11 Mathematics Ch 5: Complex Numbers and Quadratic Equations
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