Last updated at Sept. 3, 2021 by Teachoo

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Misc, 18 Find the number of non-zero integral solutions of the equation |1 โ ๐|๐ฅ = 2๐ฅ . We need to find the value of x which should be an integer but not 0 Lets first find the value of |1 โ ๐| 1 โ ๐ Complex number is of the form x + iy Where ๐ฅ = 1 ๐ฆ = โ1 |1 โ ๐| = โ(๐ฅ^2+๐ฆ2) = โ((1)2+(โ1)2) = โ(1+1) = โ2 Hence, |1 โ ๐| = โ2 Given |1 โ ๐|๐ฅ = 2๐ฅ Putting |1 โ ๐| = โ2 (โ2)๐ฅ = 2๐ฅ (โ2)๐ฅ = (โ2 ร โ2)๐ฅ (โ2)๐ฅ = (โ2)^(2 ร ๐ฅ) (โ2)๐ฅ = ใโ2ใ^( 2๐ฅ) Comparing Powers ๐ฅ = 2๐ฅ ๐ฅ โ2๐ฅ = 0 โ ๐ฅ = 0 ๐ฅ = 0 Hence, There is no non-zero integral solution

Miscellaneous

Misc 1
Important

Misc 2

Misc 3

Misc 4 Important

Misc 5 (i) Deleted for CBSE Board 2022 Exams

Misc 5 (ii) Important

Misc 6

Misc 7

Misc 8 Important

Misc 9

Misc 10 Important

Misc 11

Misc 12

Misc 13 Important Deleted for CBSE Board 2022 Exams

Misc 14

Misc 15 Important

Misc 16

Misc 17 Important

Misc 18 Important You are here

Misc 19

Misc 20 Important

Chapter 5 Class 11 Complex Numbers (Term 1)

Serial order wise

About the Author

Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 10 years. He provides courses for Maths and Science at Teachoo.