18.12. Let the functionf be entire and f(z) ∞ as z o. Showthat f must have at least one zero.18.13. Let f(z) be an entire function such that f'(z) <|z|. Show thatf(z) = a + bz2 with some constants a, b E C such that [b| < 1.18.14. Suppose f(z) is an entire function with f(z) = f(z+1)%3 f(z+i)for all z E C. Show that f (z) is a constant.18.15. Suppose f(z) and g(z) are entire functions, g(z) # 0 and |f(z)| <1g(z), z E C. Show that there is a constant c such that f(z) = cg(z).18.16. Show that an entire function whose real part is nonpositive isconstant.

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Linear Algebra: A Modern Introduction

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Author:David Poole

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18.12. Let the function f be entire and f(z) o as z o. Show that f must have at least one zero.