Check sibling questions

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


Transcript

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

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Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths and Science at Teachoo.