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Misc 18 - |1 - i|x = 2x, find non integral solutions - Proof- Solving

Misc 18 - Chapter 5 Class 11 Complex Numbers - Part 2

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Misc, 18 Find the number of non-zero integral solutions of the equation |1 – 𝑖|π‘₯ = 2π‘₯ . We need to find the value of x which should be an integer but not 0 Lets first find the value of |1 – 𝑖| 1 – 𝑖 Complex number is of the form x + iy Where π‘₯ = 1 𝑦 = βˆ’1 |1 – 𝑖| = √(π‘₯^2+𝑦2) = √((1)2+(βˆ’1)2) = √(1+1) = √2 Hence, |1 – 𝑖| = √2 Given |1 – 𝑖|π‘₯ = 2π‘₯ Putting |1 – 𝑖| = √2 (√2)π‘₯ = 2π‘₯ (√2)π‘₯ = (√2 Γ— √2)π‘₯ (√2)π‘₯ = (√2)^(2 Γ— π‘₯) (√2)π‘₯ = γ€–βˆš2γ€—^( 2π‘₯) Comparing Powers π‘₯ = 2π‘₯ π‘₯ βˆ’2π‘₯ = 0 βˆ’ π‘₯ = 0 π‘₯ = 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 12 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.