Hi having trouble with this question!
Question: Compute line integral -
$\int_\gamma \vert z \vert^2dz$
where $\gamma$ is the line segment from $2$ to $3+i$
Attempt: $\gamma(t) = (1-t)2 + t(3+i)= 2 + 2t + it$
$\gamma'(t) = 2 + i$
$\int_2^{3+i} \vert2 + 2t + it\vert^2 (2+i)dt$
Not sure how to deal with the absolute value or I guess modulus and move forward.
EDIT: I made a mistake when simplifying the parametrization, it's actually
$\int_0^{1} \vert2 + t + it\vert^2 (1+i)dt$
After fixing that and with MPW's comment realized the real part is $(2+t)$ and imaginary just $t$, integrating became easy.
Hint: $|a+bi|^2 = a^2 + b^2$, where $a$ and $b$ are real.