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Let $C$ denote the line segment from $z=i$ to $z=1$. Show that $????_{C}z_{4}dz?????42?$ Let $C$ denote the upper half of the circle $?z?=R$, where $R>2$. Show that $????_{C}z_{4}+5z_{2}+42z_{2}?1?dz????(R_{2}?1)(R_{2}?4)?R(2R_{2}+1)?$ Let $C$ denote the upper half of the circle $?z?=R$, where $R>1$. Show that $????_{C}z_{2}logz?dz???<?R?+lnR?.$

1) solution Bounds on Contour Integrals: Suppose that f(z)is a complex function, and C is a contour in the complex plane. Let the length of C be L .