For a complex valued function $\displaystyle f(z) $, could someone explain why $\displaystyle \left|\int_{C} f(z)dz\right| \leq \int_{C} |f(z)|dz $?

Shouldn't it be $\displaystyle \left|\int_{C} f(z)dz\right| \leq \int_{C} |f(z)|\cdot |dz| $?

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- Mar 21st 2010, 12:57 PMchiph588@Complex Integration
For a complex valued function $\displaystyle f(z) $, could someone explain why $\displaystyle \left|\int_{C} f(z)dz\right| \leq \int_{C} |f(z)|dz $?

Shouldn't it be $\displaystyle \left|\int_{C} f(z)dz\right| \leq \int_{C} |f(z)|\cdot |dz| $?