Q71.If ( 1−i1+i ) 2 = ( i−11+i ) 3 = 1, (m, n ∈N) then the greatest common divisor of the least values of m and n is 3 + 321 + 331 +….∞) is __________
What This Question Tests
This question requires simplifying complex numbers to their standard form, finding the least positive integer power that makes them unity, and then calculating the greatest common divisor of these powers.
Concepts Tested
Formulas Used
i^2 = -1
(a+bi)/(c+di) simplification
GCD(a,b)
📚 NCERT Sections This Tests
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📋 Question Details
- Chapter
- Complex Numbers
- Topic
- Powers of complex numbers, roots of unity
- Year
- 2020
- Shift
- 03 Sep Shift 1
- Q Number
- Q71
- Type
- Numerical
- NCERT Ref
- Class 11 Mathematics Ch 5: Complex Numbers and Quadratic Equations
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