Ex 5.2

Chapter 5 Class 11 Complex Numbers
Serial order wise

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Ex 5.2, 4 Convert the given complex number in polar form: β 1 + i Given π§ = β1+ π Let polar form be γπ§ = π (cosγβ‘ΞΈ+π sinβ‘ΞΈ) From (1) & (2) β 1+ π = r ( cosβ‘ΞΈ + π sinβ‘ΞΈ) β 1+ π = rγ cosγβ‘ΞΈ + π r sinβ‘ΞΈ Adding ( 3 ) and ( 4 ) 1 + 1 = π2 cos2 ΞΈ+ π2 sin2ΞΈ 2 = π2 ( cos2 ΞΈ+ sin2 ΞΈ) 2 = π2 Γ 1 2 = π2 β2 = π π = β2 Finding argument β 1+ π = rγ cosγβ‘ΞΈ + π r sinβ‘ΞΈ Hence, sin ΞΈ = 1/β2 & cos ΞΈ = (β 1)/β2 Hence, sin ΞΈ = 1/β2 & cos ΞΈ = (β 1)/β2 Here, sin ΞΈ is positive and cos ΞΈ is negative, Hence, ΞΈ lies in IInd quadrant Argument = 180Β° β 45Β° = 135Β° = 135Β° Γ π/180o = ( 3 π)/4 So argument of z = ( 3 π)/4 Hence π = β2 and ΞΈ = 3π/4 Polar form of z = r (cos ΞΈ + sin ΞΈ) = β2 (cos (( 3 π)/4)+ π sin(( 3 π)/4))