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

Real numbers and purely imaginary numbers are special cases of 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. In this context, a real number can be represented as $a+0i$, making the imaginary part zero, while a purely imaginary number can be expressed as $0+bi$, making the real part zero. To identify the real part and the imaginary part of a complex number, you simply look at the coefficients of $a$ (real part) and $b$ (imaginary part) in the expression $a+bi$. For example, in the complex number $3+4i$, the real part is 3, and the imaginary part is 4.