Question

Obtain the complex integral:
${\int }_{C_1}zdz$
Where $C$ is the straight line path from $z=3+i$ to $z=3+3i$.

• A. $-4+6i$
• B. $6+2i$
• C. $2i$
• D. $3+6i$

Answer 1

The correct option is A $-4+6i$

Given the figure

$I={\int }_{3+i}^{3+3i}zdz={\left[\frac{z^2}{2}\right]}_{3+i}^{3+3i}I=\frac{(3+3i{)}^2-(3+i{)}^2}{2}I=\frac{9-9+18i-9+1-6i}{2}I=\frac{-8+12i}{2}=-4+6i$

Hence the correct answer is $-4+6i$