The value of integral #$$\int_0^{1+\mathrm i}\mathrm z\;\operatorname d\mathrm z$$# along the line #$$\mathrm y=\mathrm x$$# is _____ .
1
2
#$$i$$#
0
Answer
The value of integral #$$\int_{\mathrm C}\;\overline{\mathrm z}\;\operatorname d\mathrm z$$# , where C is shortest path joining A(0, 0) to B(1, 1) , is _____ .
The value of integral #$$\int_{\mathrm C}\;\frac{3\mathrm z}{\mathrm z+2}\;\operatorname d\mathrm z$$# , where #$$\mathrm C\;:\;\left|\mathrm z\right|=1$$# , is _____ .
3
The value of integral #$$\int_{\mathrm C}\;\frac{\mathrm{dz}}{\mathrm z(\mathrm z-2)}$$#, where #$$\mathrm C\;:\;\left|\mathrm z\right|=1$$# , is _____ .
#$$2\mathrm{πi}$$#
#$$\mathrm{πi}$$#
#$$-2\mathrm{πi}$$#
#$$-\mathrm{πi}$$#
Let C be a circle #$$\left|\mathrm z-1\right|=3$$# in the complex plane, then #$$\int_{\mathrm C}\;\frac{\cos\;\mathrm z}{\mathrm z-\mathrm\pi}\;\operatorname d\mathrm z$$# , is _____ .
#$$4\mathrm{πi}$$#
none of these