Example 7.11.  Let .  Then f(z) can be factored as the product of    and  ,  which have zeros of orders and , respectively, at .  
Hence   is a zero of order 4 of  f(z).

Explore Solution 7.11.

Enter the function   and find the first few terms of the Maclaurin series.  

Thus, has a zero of order k = 4 at z = 0.

Investigate the graph for real variables.

We can use Mathematica to investigate the real and imaginary parts and the absolute value of .  

(c) 2006 John H. Mathews, Russell W. Howell