Question

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)

Explanation:

Real - numbers are a subset of complex numbers where the imaginary part is zero. Purely imaginary numbers have a real - part equal to zero. A complex number is written in the form \(a + bi\), where \(a\) is the real part and \(b\) is the coefficient of the imaginary unit \(i\). To identify the real part of a complex number \(z=a + bi\), we simply look at the value of \(a\). Since real numbers can be written as \(a+0i\) and purely imaginary numbers as \(0 + bi\), they are both complex numbers as they fit the general form \(a + bi\).

Answer:

Real numbers are complex numbers with an imaginary part of 0. Purely imaginary numbers are complex numbers with a real part of 0. A complex number is of the form \(a + bi\), and the real part is \(a\). All real and purely imaginary numbers are complex because they can be written in the \(a + bi\) form.