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Algebra

New kid on the Block

 Joined: 31 Aug 2011 Post: 13
19 May 2012 12:10:54 IST
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complex no's
Engineering Entrance , JEE Main , JEE Advanced , Mathematics , Algebra

arg(z1/z2)=arg(z1)-arg(z2)+2npi i don't understand the utility of 2npi

New kid on the Block

Joined: 31 Aug 2011
Posts: 13
2 Jun 2012 08:10:39 IST
0 people liked this

please solve this for me...

Scorching goIITian

Joined: 18 Mar 2010
Posts: 278
2 Jun 2012 09:34:24 IST
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PRINCIPAL ARGUMENT MUST BELONG TO (-pi , pi]

now z1/z2 is also complex number say ' w '

so arg(z1/z2) must also belong to (-pi , pi]     but  arg(z1)-arg(z2) is difference & can be any thing so to bring it within (-pi , pi]   we use term 2npi with suitable n

ex:- arg(z1) = pi   and  arg(z2) = -pi/2    then arg(z1)-arg(z2) =3pi/2  which in not in domain   so arg(z1/z2) =3pi/2 +2npi

for n= -1  we have arg(z1/z2) = -pi/2 which is PRINCIPAL ARGUMENT of the complex no ' w ' .................................  hope u got it..:D

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