1. Chapter 4 Class 11 Complex Numbers
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Misc 12 - Chapter 4 Class 11 Complex Numbers

Last updated at Dec. 16, 2024 by Teachoo

 

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Misc, 18 Find the number of non-zero integral solutions of the equation |1 โ€“ ๐‘–|๐‘ฅ = 2๐‘ฅ . 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 ๐‘ฅ = 1 ๐‘ฆ = โˆ’1 |1 โ€“ ๐‘–| = โˆš(๐‘ฅ^2+๐‘ฆ2) = โˆš((1)2+(โˆ’1)2) = โˆš(1+1) = โˆš2 Hence, |1 โ€“ ๐‘–| = โˆš2 Given |1 โ€“ ๐‘–|๐‘ฅ = 2๐‘ฅ Putting |1 โ€“ ๐‘–| = โˆš2 (โˆš2)๐‘ฅ = 2๐‘ฅ (โˆš2)๐‘ฅ = (โˆš2 ร— โˆš2)๐‘ฅ (โˆš2)๐‘ฅ = (โˆš2)^(2 ร— ๐‘ฅ) (โˆš2)๐‘ฅ = ใ€–โˆš2ใ€—^( 2๐‘ฅ) Comparing Powers ๐‘ฅ = 2๐‘ฅ ๐‘ฅ โˆ’2๐‘ฅ = 0 โˆ’ ๐‘ฅ = 0 ๐‘ฅ = 0 Hence, There is no non-zero integral solution
  1. Chapter 4 Class 11 Complex Numbers
  2. Serial order wise

    3. Miscellaneous

    Modulus, Argument, Polar Representation →
Modulus, Argument, Polar Representation →
Chapter 4 Class 11 Complex Numbers
Serial order wise

About the Author

Davneet Singh

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