In this paper, we focus on two particularly problematic concepts in teaching mathematics: the complex unit i and angles. These concepts are naturally linked via De Moivre's theorem but are independently misused in numerous contexts. We present definitions, notations, and ways of speaking about these terms from mathematics education that are not valid from a subject-specific point of view. We justify how these incorrectly used definitions, notations, and ways of speaking convey a false picture of the mathematical content and present options for introducing these concepts in classroom practice in a correct way.