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Last updated at Sept. 3, 2021 by Teachoo

Misc, 18 Find the number of non-zero integral solutions of the equation |1 β π|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 β π| 1 β π Complex number is of the form x + iy Where π₯ = 1 π¦ = β1 |1 β π| = β(π₯^2+π¦2) = β((1)2+(β1)2) = β(1+1) = β2 Hence, |1 β π| = β2 Given |1 β π|π₯ = 2π₯ Putting |1 β π| = β2 (β2)π₯ = 2π₯ (β2)π₯ = (β2 Γ β2)π₯ (β2)π₯ = (β2)^(2 Γ π₯) (β2)π₯ = γβ2γ^( 2π₯) Comparing Powers π₯ = 2π₯ π₯ β2π₯ = 0 β π₯ = 0 π₯ = 0 Hence, There is no non-zero integral solution