1. Class 11
2. Important Question for exams Class 11
3. Chapter 5 Class 11 Complex Numbers

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Misc 4 If x โ iy = โ((a โ ib)/(c โ id)) prove that (๐ฅ2 + ๐ฆ2)^2 = (a^2 + b^2)/(c^2 + d^2 ) Introduction (๐ฅ โ ๐๐ฆ) (๐ฅ+ ๐๐ฆ) Using ( a โ b ) ( a + b ) = a2 โ b2 = (๐ฅ)^2 โ (๐๐ฆ)2 = ๐ฅ2 โ (๐) 2๐ฆ2 = ๐ฅ2 โ (โ 1)๐ฆ2 = ๐ฅ2 + ๐ฆ2 Misc 4 If x โ iy = โ((a โ ib)/(c โ id)) prove that (๐ฅ2 + ๐ฆ2)^2 = (a^2 + b^2)/(c^2 + d^2 ) Given ๐ฅ โ ๐๐ฆ = โ((a โ ib)/(c โ id)) Calculating ๐ฅ + ๐๐ฆ Replacing โ ๐ by ๐ ๐ฅ + ๐๐ฆ = โ((a + ib)/( c + id)) Multiplying (1) &(2) (๐ฅ โ๐๐ฆ) (๐ฅ+ ๐๐ฆ) = โ((a โ ib)/(c โ id)) ร โ((a + ib)/(c + id)) ๐ฅ2+๐ฆ2 =โ((aโib)/(cโid)ร(a + ib)/(c + id)) =โ((( a โ ib) (a + ib))/((c โ id) (c + id))) Using ( a โ b ) ( a + b ) = a2 โ b2 =โ(((a)^2 โ (ib)^2 )/((c)^2โใ (id)ใ^2 )) =โ((a^2 โ i^2 b^2 )/(c^2 โ i^2 d^2 )) Putting i2 = โ1 =โ((a2โ(โ1) b2 )/(c2โ(โ1)d2)) =โ((a2+ b2 )/(c + d2)) Hence, ๐ฅ2 + ๐ฆ2 =โ((a2+ b2 )/(c2 + d2)) Squaring both sides (x2 + y2)2 =(โ((a2+ b2 )/(c2 + d2)))^2 (x2 + y2)2 = (a2+ b2 )/(c2 + d2) Hence Proved

Chapter 5 Class 11 Complex Numbers

Class 11
Important Question for exams Class 11