# Misc 20

Last updated at March 9, 2017 by Teachoo

Last updated at March 9, 2017 by Teachoo

Transcript

Misc, 20 If ((1 + ๐)/(1 โ ๐))^๐ = 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 + ๐)/(1 โ ๐)) (1 + ๐)/(1 โ ๐) Rationalizing = (1 + ๐)/(1 โ ๐) ร (1 + ๐)/(1 + ๐) = ((1 + ๐) (1 + ๐))/((1 โ ๐)(1 + ๐)) = (1 + ๐ )2/((1)2 โ (๐)2) = (1 + (๐)2 + 2 ร 1 ร ๐)/(1 โ ๐2) = (1 + ๐2 + 2๐)/(1 โ ๐2) Putting i2 = โ1 = (1+ (โ1) + 2๐)/(1 โ(โ1) ) = (1 โ 1+ 2๐)/(1+1) = (0 + 2๐)/2 = 2๐/2 = ๐ ย Hence, (1 + ๐)/(1 โ ๐) = ๐ Given ((1 + ๐)/(1 โ ๐))^๐ = 1 (๐)๐ = 1 We know that ๐2 = โ1 Squaring both sides (๐2)2 = (โ1)2 ๐4 = 1 Hence the minimum value of m which satisfies the equation is 4 ย

Class 11

Important Question 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

About the Author

CA Maninder Singh

CA Maninder Singh is a Chartered Accountant for the past 8 years. He provides courses for Practical Accounts, Taxation and Efiling at teachoo.com .