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  1. Class 11
  2. Important Question for exams Class 11

Transcript

Ex 5.1, 10 Express the given Complex number in the form a + ib: (โˆ’2โˆ’1/3 ๐‘–)^3 (โˆ’2โˆ’1/3 ๐‘–)^3 = โˆ’ 1 (2+1/3 ๐‘–)^3 = โˆ’ (2+1/3 ๐‘–)^3 It is of the form (a + b)3 Using (a + b)3 = a3 + b3 + 3 ab (a + b) Here a = 2 and b = 1/3 i = โˆ’((2)^3+(1/3 ๐‘–)^3+3 ร—2ร—1/3 ๐‘–(2+1/3 ๐‘–)) = โˆ’(8+(1/3)^3ร—(๐‘–)^3+2๐‘–(2+1/3 ๐‘–)) = โˆ’(8+1/27 ๐‘–^3+4๐‘–+2/3 ๐‘–^2 ) = โˆ’(8+1/27 ใ€–๐‘–ร—๐‘–ใ€—^2+4๐‘–+2/3 ๐‘–^2 ) Putting ๐‘–^2=โˆ’1 = โˆ’1 (8+1/27 ๐‘–(โˆ’1)+4๐‘–+2/3 (โˆ’1)) = โˆ’1 (8โˆ’1/27 ๐‘–+4๐‘–โˆ’2/3) = โˆ’ 8 + 1/27 ๐‘– โˆ’ 4i + 2/3 = โˆ’ 8 + 2/3 + ( 1)/27 ๐‘– โ€“ 4๐‘– = (โˆ’ 8+ 2/3) + (( 1)/27โˆ’4)๐‘– = ((โˆ’24 + 2)/3) + ((1 โˆ’ 4 ร—27)/27)๐‘– = (โˆ’22)/3 + ((1 โˆ’108)/27)๐‘– = (โˆ’22)/3 + (( โˆ’107)/27)๐‘– = (โˆ’22)/3 โˆ’ ( 107)/27 ๐‘–

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Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 9 years. He provides courses for Maths and Science at Teachoo.