Ex 5.2

Chapter 5 Class 11 Complex Numbers
Serial order wise

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Ex5.2, 3 Convert the given complex number in polar form: 1 β i Given π§ = 1 β π Let polar form be z = π (cosβ‘ΞΈ+π sinβ‘ΞΈ ) From (1) and (2) 1 - π = r (cos ΞΈ + π sin ΞΈ) 1 β π = r cos ΞΈ + π r sin ΞΈ Comparing real part 1 = r cos ΞΈ Squaring both sides (1)2 =( π cosβ‘ΞΈ )^2 1 = π2 cos2ΞΈ Adding (3) and (4) 1 + 1 = π2 cos2 ΞΈ + π2 sin2 ΞΈ 1 + 1 = r2 cos2 ΞΈ + r2 sin2 ΞΈ 2 = r2 ( cos2 ΞΈ + sin2 ΞΈ ) 2 = r2 Γ 1 2 = r2 β2 = r r = β2 Now finding argument 1 β π = r cos ΞΈ + π r sin ΞΈ Comparing real part 1 = r cos ΞΈ Putting r =β2 1 = β2 cos ΞΈ 1/β2 = cos ΞΈ cos ΞΈ = 1/β2 Hence, cos ΞΈ = 1/β2 & sin ΞΈ = (β 1)/β2 Hence, cos ΞΈ = 1/β2 & sin ΞΈ = (β 1)/β2 Since, sin ΞΈ is negative and cos ΞΈ is positive, Hence, ΞΈ lies in IVth quadrant Argument = β 45Β° = β 45Β° Γ π/(180Β°) = (β π)/4 Hence, argument of π§ = (β π)/4 Hence π = β2 and ΞΈ = ( β π)/4 Polar form of π§=π (cosβ‘ΞΈ+sinβ‘ΞΈ ) = β2 (cos(( β π)/4)+sin(( β π)/4))

#### Davneet Singh

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.