In 3–5 sentences, describe why real numbers and purely imaginary numbers are also complex numbers composed of real and imaginary parts. Also, describe how to identify the real part versus the imaginary part of a complex number. ???????????????

Answer 1

Complex numbers are expressed in the form \( a + bi \), where \( a \) is the real part and \( b \) is the coefficient of the imaginary unit \( i \). Real numbers can be considered as complex numbers with an imaginary part of zero (e.g., \( a + 0i \)), while purely imaginary numbers have a real part of zero (e.g., \( 0 + bi \)). To identify the real and imaginary parts in a complex number, look for the coefficient of \( i \); the term without \( i \) represents the real part, and the term with \( i \) represents the imaginary part. For instance, in the complex number \( 3 + 4i \), 3 is the real part and 4 is the imaginary part.