cosz=(e^(iz)+e^(-iz))/2

Therefore, if p = e (iz), the original equation becomes

p^2-4p+ 1=0

p=2 √3

e^(iz)=2 √3

Take the logarithm of both sides and get

iz=ln(2 √3)+2kπi，k∈Z

z=-iln(2 √3)+2kπ，k∈Z

Complex variable function refers to a function with complex numbers as independent and dependent variables, and the related theory is complex variable function theory. Analytic function is a kind of analytic function in complex variable function. Complex variable function theory mainly studies analytic functions in complex number field, so it is usually called analytic function theory.

General situation of development

The theory of complex variable function came into being in18th century. 1774, Euler considered two equations derived from the integration of complex variables in one of his papers. Before him, French mathematician D'Alembert had obtained them in his paper on fluid mechanics. Therefore, people later mentioned these two equations and called them "D'Alembert-Euler equations".