Pronunciation: [ɹˈi͡əl pˈɑːt] (IPA) 
The spelling of the words "real part" is straightforward. The word "real" is spelled r-e-a-l, while the word "part" is spelled p-a-r-t. In IPA phonetic transcription, "real" would be transcribed as /riːl/ and "part" as /pɑːt/. "Real" is pronounced with a long "ee" sound, and "part" uses an open "a" sound. Together, the phrase "real part" is pronounced as /riːl pɑːt/ and refers to the non-imaginary portion of a complex number.
The term "real part" is a mathematical concept that refers to the real component or the real portion of a complex number. In mathematics, a complex number is a number that comprises a real part and an imaginary part. The real part of a complex number is the part that solely consists of real numbers.
The real part of a complex number, denoted as Re(z), is obtained by considering the horizontal axis on the complex plane. It represents the horizontal distance of the complex number from the origin (0,0) along the real axis. The real part is responsible for specifying the magnitude and direction of the number on the real line.
For example, in the complex number z = 3 + 4i, the real part is 3. This indicates that the number is located three units to the right of the origin. In contrast, if the real part is zero, the complex number lies entirely on the imaginary axis.
The real part plays a fundamental role in various mathematical operations involving complex numbers, such as addition, subtraction, and multiplication. It provides a crucial component for visualizing and understanding complex numbers in the complex plane. By isolating the real part from an imaginary part, mathematicians can analyze and manipulate complex numbers more effectively to solve equations and model real-world phenomena.
The term "real part" comes from mathematics and specifically refers to the real component of a complex number. The word "real" is derived from the Latin word "realis", meaning "actual" or "genuine". In the context of complex numbers, the real part represents the portion of the number that is not imaginary but corresponds to a real value on the number line.
