The book, containing a wealth of illustrative material,
acquaints the reader with complex numbers and operations 
on them and also with conformal mappings, that is mappings
which preserve the angles (they are employed in cartography, 
mechanics, physics).

After seeing two books Areas and Logarithms | Remarkable Curves we now come to Complex Numbers and Conformal Mappings by A. I. Markushevich in the  Little Mathematics Library. We will in the future see more books from him.

The book acquaints the reader with complex numbers and
functions of a complex argument (including Zhukovsky’s function as applied to the construction of a wing section). The material is presented in a geometric form. Complex numbers are considered as directed line segments and functions as mappings. To prepare the reader to such an understanding of complex numbers, we begin with a geometric interpretation of real numbers and operations on them. The book is based on a lecture delivered by the author to high-school students. To read the book, the reader need not be acquainted with complex numbers.

It is intended for all those who are
interested in mathematics and primarily for high-school
students, it can also be of use for self-education. For proper
comprehension of the content of the book the reader must posses
high-school knowledge of mathematics.

The book was translated from the Russian by Irene Aleksanova and was first published by Mir in 1982. This book was also part of the Public Lectures in Mathematics – Volume 8 (PLM) which was published in 1960’s. Link below is for the Mir version.

PDF | OCR | Cover | Bookmarked | 4.4 MB | 68 pp | 600 dpi

You can get the book here.

For Magnet / Torrent Links go here.

Contents:

Foreword
Sections 1 to 34
Problems and Solution