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1

MAT334--Lectures & Home Assignments / Re: Chapter 2.1 PG 80

« on: October 17, 2018, 06:42:40 PM »

I think what the textbook is trying to say is that even though you could find a function f(z) whose real part can be written as u(x,y), but f(z) does not have to be analytic.

2

Quiz-1 / Re: Q1: TUT 5201

« on: September 28, 2018, 05:49:13 PM »

Let $z=x+yi $
Then the equation can be rewritten as:
\begin{gather*}
|(x+yi)+1|^2+2|x+yi|^2=|(x+yi)-1|^2\\
|(x+1)+yi|^2+2|x+yi|^2=|(x-1)+yi|^2\\
(x+1)^2+y^2+2x^2+2y^2=(x-1)^2+y^2\\
3x^2+2x+3y^2+1=x^2-2x+y^2+1\\
2x^2+2y^2+4x=0\\
(x+1)^2+y^2=1
\end{gather*}
Therefore, the locus is circle centered at $(-1,0)$ with radius $1$
Fixed formatting. V.I.