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Question Number 127364 by mohammad17 last updated on 29/Dec/20
prove that: Arg(log(3−4i))=(1/i)log(((3−4i)/5)) help me sir please
provethat:Arg(log(3−4i))=1ilog(3−4i5)helpmesirplease
Commented by mohammad17 last updated on 29/Dec/20
pleas help me ?
pleashelpme?
Answered by ebi last updated on 29/Dec/20
z=log(3−4i)=log(a+bi) let a+bi=re^(iθ) (convert to polar form) where r=(√(a^2 +b^2 )) and θ=arg(a+bi) r=(√(3^2 +(−4)^2 ))=(√(25))=5 log(3−4i)=log(5e^(iθ) ) log(3−4i)=log(5)+iθ iθ=log(3−4i)−log(5) iθ=log(((3−4i)/5)) θ=(1/i)log(((3−4i)/5)) ∴ arg(3−4i)=(1/i)log(((3−4i)/5))
z=log(3−4i)=log(a+bi)leta+bi=reiθ(converttopolarform)wherer=a2+b2andθ=arg(a+bi)r=32+(−4)2=25=5log(3−4i)=log(5eiθ)log(3−4i)=log(5)+iθiθ=log(3−4i)−log(5)iθ=log(3−4i5)θ=1ilog(3−4i5)∴arg(3−4i)=1ilog(3−4i5)
Commented by mohammad17 last updated on 29/Dec/20
you are a wonderful person ,thank you sir
youareawonderfulperson,thankyousir

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