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Misc 14 - Chapter 5 Class 11 Complex Numbers (Important Question)
Last updated at Dec. 16, 2024 by Teachoo
Class 11
Important Questions for exams Class 11
- Chapter 1 Class 11 Sets
- Chapter 2 Class 11 Relations and Functions
- Chapter 3 Class 11 Trigonometric Functions
- Chapter 4 Class 11 Mathematical Induction
-
Chapter 5 Class 11 Complex Numbers
- Chapter 6 Class 11 Linear Inequalities
- Chapter 7 Class 11 Permutations and Combinations
- Chapter 8 Class 11 Binomial Theorem
- Chapter 9 Class 11 Sequences and Series
- Chapter 10 Class 11 Straight Lines
- Chapter 11 Class 11 Conic Sections
- Chapter 12 Class 11 Introduction to Three Dimensional Geometry
- Chapter 13 Class 11 Limits and Derivatives
- Chapter 14 Class 11 Mathematical Reasoning
- Chapter 15 Class 11 Statistics
- Chapter 16 Class 11 Probability
Transcript
Misc, 20 If ((1 + )/(1 ))^ = 1, then find the least positive integral value of m. We need to find minimum value of m which is positive as well as integer. Lets first find the value of ((1 + )/(1 )) (1 + )/(1 ) Rationalizing = (1 + )/(1 ) (1 + )/(1 + ) = ((1 + ) (1 + ))/((1 )(1 + )) = (1 + )2/((1)2 ( )2) = (1 + ( )2 + 2 1 )/(1 2) = (1 + 2 + 2 )/(1 2) Putting i2 = 1 = (1+ ( 1) + 2 )/(1 ( 1) ) = (1 1+ 2 )/(1+1) = (0 + 2 )/2 = 2 /2 = Hence, (1 + )/(1 ) = Given ((1 + )/(1 ))^ = 1 ( ) = 1 We know that 2 = 1 Squaring both sides ( 2)2 = ( 1)2 4 = 1 Hence the minimum value of m which satisfies the equation is 4
