1. ## [SOLVED] Complex

Which of the following functions are entire? Give reasons.

(i) f(z) = sin |z|,

(ii) f(z) = $z^5 + iz^7 + z^{12},$

(iii) f(z) = f(x + iy) = x,

(iv) f(z) = 2.

2. How would I know if the function is entire?

3. Originally Posted by ronaldo_07
How would I know if the function is entire?
You would test it by applying the definition .....

4. what definition would I use I have no clue.

5. Originally Posted by ronaldo_07
what definition would I use I have no clue.
Entire function - Wikipedia, the free encyclopedia

6. Originally Posted by ronaldo_07
(i) f(z) = sin |z|
This function is bounded, so if it was entire then it would be a constant.
This is a contradiction so it is not entire.

(ii) f(z) = $z^5 + iz^7 + z^{12},$
Polynomials are always entire.

(iii) f(z) = f(x + iy) = x
Check the Cauchy-Riemann equations

(iv) f(z) = 2.
Polynomials are always entire.