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Question Number 113091 by bobhans last updated on 11/Sep/20
What is the area bounded by the curves  arg(z) = (π/3) ; arg(z)= ((2π)/3) and arg(z−2−2i(√3))=π  on the complex plane?
Whatistheareaboundedbythecurvesarg(z)=π3;arg(z)=2π3andarg(z22i3)=πonthecomplexplane?
Answered by john santu last updated on 11/Sep/20
 (i) arg (z) = (π/3) → (y/x) = tan ((π/3))         y = x(√3)     (ii) arg (z) = ((2π)/3)→(y/x) = tan (((2π)/3))       y = −x(√3)   (iii) arg (z−2−2i(√3) )= π      ((y−2(√3))/(x−2)) = tan π →y = 2(√3)  Hence the area is = 2×(1/2)×2×2(√3) = 4(√3)
(i)arg(z)=π3yx=tan(π3)y=x3(ii)arg(z)=2π3yx=tan(2π3)y=x3(iii)arg(z22i3)=πy23x2=tanπy=23Hencetheareais=2×12×2×23=43

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