Final answer:
The method of research that involves in-depth investigation of the individual peculiarities of interviewees, as conducted by Sigmund Freud, is called a case study.
Step-by-step explanation:
The method of research Sigmund Freud used by conducting in-depth interviews over an extended period of time with a few clients is best defined as a case study. A case study is a deep exploration of an individual or a small group in their own context, often involving qualitative methods such as interviews, observations, and sometimes quantitative data. This approach allows researchers to gain a deep understanding of the unique aspects and complexities of a person's or group's experiences and behaviors.
To illustrate, if we consider the analogy of different people describing a person from their own perspectives, it relates to how a case study allows for a detailed and multifaceted view of an individual, enriched by the perspectives and insights of those conducting the study. Whether it's using interviews or other sources, the main answer for this type of research is a case study, as it dives into the rich, detailed understanding of the participant, going beyond what might be captured through large-scale surveys or observations.