1) Give the points at which the given function is not analytic; z z + 3i...

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1) Give the points at which the given function is not analytic; z z + 3i a) f(z) = b) f(z) = c) f(z) = d) f(z) = b) lim z →1 2i z² - 2z +5iz z²+z z + 4 2) Show that f(2)=z and f(2)= z.zare both nowhere differentiable 3) Show that the given limit does not exist a) lim z+5-7i z² +62 +25 b) f(z) = x+y=1 z - 1 4) Using the analyticity criterion show that the given functions are analytic, stating the appropriate domains and find f'(z) x-1 a) f(z)=- (x-1)² + y² x²³ + xy² + x x² + y² - y (x - 1)² + y² - x²y + y² − y x² + y² c) f(z) = e(cos y + i sin y) d) f(z)=z³ e) f(z) = sin z 5) Show that the Cauchy - Riemann equations in polar coordinates are: du dr du 20 11 = ete šle r de dr 1) Give the points at which the given function is not analytic; z z + 3i a) f(z) = b) f(z) = c) f(z) = d) f(z) = b) lim z →1 2i z² - 2z +5iz z²+z z + 4 2) Show that f(2)=z and f(2)= z.zare both nowhere differentiable 3) Show that the given limit does not exist a) lim z+5-7i z² +62 +25 b) f(z) = x+y=1 z - 1 4) Using the analyticity criterion show that the given functions are analytic, stating the appropriate domains and find f'(z) x-1 a) f(z)=- (x-1)² + y² x²³ + xy² + x x² + y² - y (x - 1)² + y² - x²y + y² − y x² + y² c) f(z) = e(cos y + i sin y) d) f(z)=z³ e) f(z) = sin z 5) Show that the Cauchy - Riemann equations in polar coordinates are: du dr du 20 11 = ete šle r de dr

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1 a The function fz zz 3i is not analytic at z ... View the full answer