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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 )`

.