This article is devoted to the methods of teaching conformal mapping using a linear function of
complex variables. A brief history of the concept of a function of a complex variable and its application in various
mathematical disciplines is given. We consider the definition of a conformal linear function and its special cases, which
are closely related to a simple transformation of the plane. The geometric value of the transformation of an entire linear
function of complex variables is shown using problems. Special attention is paid to the method of conducting a practical
lesson on "the Whole linear function of complex variables", for which tasks on Bloom's taxonomy were compiled.