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

Complex numbers are defined as numbers that can be expressed in the form \(a + bi\), where \(a\) and \(b\) are real numbers, and \(i\) is the imaginary unit defined as the square root of -1. Real numbers can be seen as complex numbers with an imaginary part of zero (i.e., \(a + 0i\)), while purely imaginary numbers have a zero real part (i.e., \(0 + bi\)). To identify the real and imaginary parts of a complex number, one simply separates the expression into its components: the real part is the coefficient of the non-imaginary term \(a\), and the imaginary part is the coefficient \(b\) that multiplies \(i\). For instance, in the complex number \(3 + 4i\), the real part is 3 and the imaginary part is 4.