contour integration problem..

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how can we find $$\int_C e^{2z} 9^{z-2} dz,$$ where $C$ is the the contour from $z = 0$ to $z = 1 − i$

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HINT:

$$e^{2z}9^{2-z}=81e^{2(1-\log 3)z}$$

and $e^z$ is analyic. So, the integral is path independent.