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                <h1>Curves in the complex plane</h1>

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                    Suppose the continuous real-valued functions $x = x(t),$ $y = y(t),$ $a \leq t \leq b,$ are
                    parametric
                    equations of a curve $C$ in the complex plane. If we use these equations as the real and
                    imaginary parts in $z = x+iy,$ we can describe
                    the points $