Question

what is the integral along c of following Re z dz where c is the shortest path from 1+i to 3+2i.

Answer 1

I suggest drawing a picture

Answer 2

i didn't get what you said

Answer 3

solve it using cauchy integral formula or theorem etc.

Answer 4

The first thing to do here is to find the parametrization of the given curve, which is given by:
\(z(t)=1+i+t(3+2i-1-i)=1+i+t(2+i)\).

Answer 5

For the parametrization above: \(0\le t\le 1\)

Answer 6

You probably know the formula:
\[\int\limits_{\zeta}f(z)dz=\int\limits_{a}^{b}f(z(t))z'(t)dt\]
where \(z(t)\) is the parametrization of \(\zeta\).

Answer 7

Now all we need is a direct substitution with \(z(t)=1+i+t(2+i)\), \(z'(t)=2+i\), \(a=0\) and \(b=1\).

Answer 8

thanks alot plz answer my second question