Doubt

[Bhupender Rana]

Where is the function Arg(z^2 + 1) discontinuous?

[Sarita Math]

Whenever you can't understand the structure of a complex function or facing some difficulties, transform it into Cartesian co-ordinate and treat it as the functions in R x R in several variables. It may help you. Anyways, see the attach file.

 

[Bhupender Rana]

But the answer in Jain and Iyenger is given as Im(z^2 + 1)=0 and Re(z^2 + 1) <= 0. I also got the same answer as yours. 

On Sat, Nov 17, 2012 at 11:03 AM, Sarita Math <sarita...@gmail.com> wrote:

Whenever you can't understand the structure of a complex function or facing some difficulties, transform it into Cartesian co-ordinate and treat it as the functions in R x R in several variables. It may help you. Anyways, see the attach file.

 

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[AMAN GUPTA]

then how do we define argument of i??????/

On Sat, Nov 17, 2012 at 11:03 AM, Sarita Math <sarita...@gmail.com> wrote:

Whenever you can't understand the structure of a complex function or facing some difficulties, transform it into Cartesian co-ordinate and treat it as the functions in R x R in several variables. It may help you. Anyways, see the attach file.

 

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[Bhupender Rana]

I have another doubt. If f(z) is an analytic function show that log |f(z)| is a harmonic function.

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[Sarita Math]

see the attach file.

@Bhupender,

What process we proceed before, there one part was missing which was Re (z^2+1) <0.

@Aman:

arg(i)=

any complex number z we can write, 

where r=|z| and =arg(z)

then

 

or, see the attach file.

[Bhupender Rana]

Thank You, Mam!!

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[vijay singh nishad]

      

i am solving this problem through polar form of c.r. equation and getting wrong result

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[Sarita Math]

See the attach file