293 6.4 Zeros and Poles In Problems 11-14, the indicated number is a zero of the given function. Use a Maclaurin or Taylor series to determine the order of the zero. 11. f(z) = z(1 cos² z); z = 0 13. f(z) = 1 e²-1; z = 1 12. f(z) =z sin z; z = 0 14. f(z) = 1 лi+z+е²; z=лi In Problems 15-26, determine the order of the poles for the given function. 3z 1 15. f(z) = 6 z² + 2z+5 16. f(z) = 5- z² 17. f(z) = 1+ 4i (z+2)(z+i)4 18. f(z) = z-1 (z+1)(z³ + 1) 19. f(z) = tanz 20. f(z) = z² 1 - cosh z 21. f(z) = 22. f(z) = 1 24. f(z) = 23. f(z) = e² - 1 z² 1+e² COS Z- cos 2z sin z 26. f(z) = 25. f(z) = z6 z² - z subiash In Problems 27 and 28, show that the indicated number is an essential singularity of the given function. 27. f(z) = z³ sin ;z=0 Z 28. f(z) = (z 1) cos = (2 + 2) iz O is an essential singularity of f(z) = e²+1/2