Misc 12 - Chapter 4 Class 11 Complex Numbers

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Misc 12 - |1 - i|x = 2x, find non integral solutions - Miscellaneous - Miscellaneous

part 2 - Misc 12 - Miscellaneous - Serial order wise - Chapter 4 Class 11 Complex Numbers

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Misc, 18 Find the number of non-zero integral solutions of the equation |1 ā€“ š‘–|š‘„ = 2š‘„ . We need to find the value of x which should be an integer but not 0 Lets first find the value of |1 ā€“ š‘–| 1 ā€“ š‘– Complex number is of the form x + iy Where š‘„ = 1 š‘¦ = āˆ’1 |1 ā€“ š‘–| = āˆš(š‘„^2+š‘¦2) = āˆš((1)2+(āˆ’1)2) = āˆš(1+1) = āˆš2 Hence, |1 ā€“ š‘–| = āˆš2 Given |1 ā€“ š‘–|š‘„ = 2š‘„ Putting |1 ā€“ š‘–| = āˆš2 (āˆš2)š‘„ = 2š‘„ (āˆš2)š‘„ = (āˆš2 Ɨ āˆš2)š‘„ (āˆš2)š‘„ = (āˆš2)^(2 Ɨ š‘„) (āˆš2)š‘„ = 怖āˆš2怗^( 2š‘„) Comparing Powers š‘„ = 2š‘„ š‘„ āˆ’2š‘„ = 0 āˆ’ š‘„ = 0 š‘„ = 0 Hence, There is no non-zero integral solution

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Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science and Computer Science at Teachoo