Let the function f CC be a doubly periodic function, which means that for non-zero complex numbers a, ß, with a/ẞ & R, f(z+a) = f(z+Bẞ) = f(z) for all z = C. Prove that every entire function that is doubly periodic is constant.

Q: (a) {z: |z+2i| 6}

A: I have solved by drawing the diagrams. See the step 2

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A: Answer given below in great detail.

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Q: (16) Show that: (1) The function f(z) is continuous in all complex plane. (2) (-1+i)-8(1+i).

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A: We have to prove that every polynomial of degree atleast 1 takes every complex value a in C .

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A: We can start by using the definition of theta notation to prove these statements. Recall that theta…

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Q: (1) Let f(x) = 1,x > 0 with domf= R4+. Find the conjugate of function f(x). %3D

A: given fx=1x , x>0 with domf=R++ claim- find the conjugate of function fx