Logaritmo de números reais negativos: uma proposta didática para a série final do Ensino Médio

Abstract

This paper proposes a teaching sequence to the student who is finishing High school so that it can respond clearly and effectively whether or not logarithm of negative real number. In the first year of high school, the definitions and properties of logarithms are presented only for positive real numbers. Students finish high school and the connection of logarithms and complex numbers is not done to show that there are rather logarithms of negative real numbers, then these students complete their basic education believing that there is no logarithm of negative numbers. From this perspective we developed a didactic sequence, making the connection between the history of mathematics, complex numbers, logarithmic, exponential functions and also the Euler equation, in order to show that there are logarithms of negative real numbers. But the solution will not be real, as some believed mathematicians of the seventeenth and eighteenth centuries, but an imaginary number.