Problem 2: Given a complex number z=x+iy in rectangular form, we define e^(z) to be e^(z)=e^(x)e^(iy), and recall that e^(iy) was previously defined through Euler's formula. (a) Write the function f(z)=e^(z) as f(z)=u(x,y)+iv(x,y). (b) Use your answer to part (a) to show that lim_(z-2+i pi )e^(z)=e^(2+i pi ).

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Problem 2: Given a complex number z=x+iy in rectangular form, we define e^(z) to be e^(z)=e^(x)e^(iy), and recall that e^(iy) was previously defined through Euler's formula. (a) Write the function f(z)=e^(z) as f(z)=u(x,y)+iv(x,y). (b) Use your answer to part (a) to show that  lim_(z->2+i pi )e^(z)=e^(2+i pi ).

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