homeworks and attendance quizzes for kang

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+1)
+
+(z^2+3)/((z+1)(z^2+5))
+
+Product rule, chain rule, and power rule can be used to find a
+derivative except where the function is undefined, (z+1)(z^2+5) = 0.
+These are z = -1, \pm\sqrt{5}
+
+2)
+
+f(x+iy) = xy + iy
+
+Ux = y
+Uy = x
+Vx = 0
+Vy = i
+
+Ux = Vy? y is a real number, so it is not equal to i. This is,
+therefore, not analytic.
+
+3)
+
+f(z) = z^2 = x^2 + 2xyi - y^2
+
+Ux = 2x
+Uy = -2y
+Vx = 2y
+Vy = 2x
+
+Ux = Vy? Yes.
+Uy = -Vx? Yes.
+
+This function is analytic everywhere on the plane.