Question

Obtain the complex integral:
${\int }_{C_2}zdz$
Where $C_2$ is the straight line path from $z=1+i$ to $z=3+3i$.

• A. $4+4i$
• B. $2+4i$
• C. $8i$
• D. $4$

Answer 1

The correct option is C $8i$

${\int }_{C_2}zdz={\left[\frac{z^2}{2}\right]}_{C_2}$

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

$=\frac{9+18i+9i^2-(1+2i+i^2)}{2}$

$=\frac{9+18i-9-1-2i+1}{2}$

$=\frac{16i}{2}$

$=8i$