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.(4 points)

Answer 1

Real numbers and purely imaginary numbers are considered complex numbers because they can be expressed in the standard form of a complex number, which is \( a + bi \), where \( a \) and \( b \) are real numbers, and \( i \) is the imaginary unit. For a real number, \( b = 0 \) (e.g., \( 5 \) can be written as \( 5 + 0i \)), and for a purely imaginary number, \( a = 0 \) (e.g., \( 3i \) can be written as \( 0 + 3i \)). To identify the real part of a complex number \( a + bi \), look at the coefficient \( a \), and to find the imaginary part, look at the coefficient \( b \) associated with \( i \). For example, in the complex number \( 4 - 7i \), the real part is \( 4 \) and the imaginary part is \( -7 \).