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Ex 5.1, 10 - Express in a + ib: (-2 - 1/3i)3 - Chapter 5

Ex 5.1, 10 - Chapter 5 Class 11 Complex Numbers - Part 2
Ex 5.1, 10 - Chapter 5 Class 11 Complex Numbers - Part 3

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Ex 5.1, 10 Express the given Complex number in the form a + ib: (−2−1/3 𝑖)^3 (−2−1/3 𝑖)^3 = − 1 (2+1/3 𝑖)^3 = − (2+1/3 𝑖)^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 = −((2)^3+(1/3 𝑖)^3+3 ×2×1/3 𝑖(2+1/3 𝑖)) = −(8+(1/3)^3×(𝑖)^3+2𝑖(2+1/3 𝑖)) = −(8+1/27 𝑖^3+4𝑖+2/3 𝑖^2 ) = −(8+1/27 〖𝑖×𝑖〗^2+4𝑖+2/3 𝑖^2 ) Putting 𝑖^2=−1 = −1 (8+1/27 𝑖(−1)+4𝑖+2/3 (−1)) = −1 (8−1/27 𝑖+4𝑖−2/3) = − 8 + 1/27 𝑖 − 4i + 2/3 = − 8 + 2/3 + ( 1)/27 𝑖 – 4𝑖 = (− 8+ 2/3) + (( 1)/27−4)𝑖 = ((−24 + 2)/3) + ((1 − 4 ×27)/27)𝑖 = (−22)/3 + ((1 −108)/27)𝑖 = (−22)/3 + (( −107)/27)𝑖 = (−22)/3 − ( 107)/27 𝑖

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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.