Question

Obtain the complex integral:
${\int }_{C}zdz$
Where $C$ is the straight line path from $z=1+i$ to $z=3+i$.

• A. $2$
• B. $4+i$
• C. $4+2i$
• D. $2+2i$

Answer 1

Answer: (C)

$4+2i$

${\int }_{C}zdz={\left[\frac{z^2}{2}\right]}_C$

Substituting the upper and lower limits, we get $(3+i{)}^2-(1+i{)}^2$

$=\frac{9+6i+i^2-(1+2i+i^2)}{2}$

$=\frac{9+6i-1-1-2i+1}{2}$

$=4+2i$