Let f(z) be an analytic function defined on the complex plane, where z=x+iy and ii is the imaginary unit. The function f(z) is given by f(z)=e^{z^2}, where ee is the base of the natural logarithm. Calculate the derivative of f(z) at the point z=1+i.

Let f(z) be an analytic function defined on the complex plane, where z=x+iy and ii is the imaginary unit. The function f(z) is given by f(z)=e^{z^2}, where ee is the base of the natural logarithm. Calculate the derivative of f(z) at the point z=1+i.

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter4: Calculating The Derivative

Section4.2: Derivatives Of Products And Quotients

Problem 37E

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Question

Let f(z) be an analytic function defined on the complex plane, where z=x+iy and ii is the imaginary unit. The function f(z) is given by f(z)=e^{z^2}, where ee is the base of the natural logarithm.

Calculate the derivative of f(z) at the point z=1+i.

Expert Solution