Ex 5.2, 4 - Convert in polar form: -1 + i - Complex number - Ex 5.2

Ex 5.2, 4 - Chapter 5 Class 11 Complex Numbers - Part 2
Ex 5.2, 4 - Chapter 5 Class 11 Complex Numbers - Part 3 Ex 5.2, 4 - Chapter 5 Class 11 Complex Numbers - Part 4 Ex 5.2, 4 - Chapter 5 Class 11 Complex Numbers - Part 5

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Question 4 Convert the given complex number in polar form: – 1 + i Given 𝑧 = −1+ 𝑖 Let polar form be 〖𝑧 = 𝑟 (cos〗⁡θ+𝑖 sin⁡θ) From (1) & (2) − 1+ 𝑖 = r ( cos⁡θ + 𝑖 sin⁡θ) − 1+ 𝑖 = r〖 cos〗⁡θ + 𝑖 r sin⁡θ Adding ( 3 ) and ( 4 ) 1 + 1 = 𝑟2 cos2 θ+ 𝑟2 sin2θ 2 = 𝑟2 ( cos2 θ+ sin2 θ) 2 = 𝑟2 × 1 2 = 𝑟2 √2 = 𝑟 𝑟 = √2 Finding argument − 1+ 𝑖 = r〖 cos〗⁡θ + 𝑖 r sin⁡θ Hence, sin θ = 1/√2 & cos θ = (− 1)/√2 Hence, sin θ = 1/√2 & cos θ = (− 1)/√2 Here, sin θ is positive and cos θ is negative, Hence, θ lies in IInd quadrant Argument = 180° – 45° = 135° = 135° × 𝜋/180o = ( 3 𝜋)/4 So argument of z = ( 3 𝜋)/4 Hence 𝑟 = √2 and θ = 3𝜋/4 Polar form of z = r (cos θ + sin θ) = √2 (cos (( 3 𝜋)/4)+ 𝑖 sin(( 3 𝜋)/4))

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Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.