Last updated at Dec. 8, 2016 by Teachoo

Transcript

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

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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.