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It is simple one. In my school book it says enter image description here

is there any mistake here? Because i think otherwise.

btw question is showing $ \int_{γ}(c_1f+c_2g)=c_1\int_{γ}f+c_2\int_{γ}g$

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Yes, clearly these are mistakes. –  Robert Israel Dec 23 '12 at 23:35
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up vote 0 down vote accepted

Just at a superficial glance, I see you (if the pencil is you) made a good correction. The reason for this is that

$$(u+i v) (x' + i y') = (u x' - v y') + i (v x' + u y') $$

The term $(u x'+v y')$ makes no sense, and is the result of a clear error.

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