Video: Understanding the Definitions of Real, Imaginary, and Complex Numbers

Video Transcript

Is the following statement true or false? Any real number is also a complex number.

We know that a complex number 𝑧 is of the form 𝑎 plus 𝑏𝑖, where 𝑎 and 𝑏 are real numbers. Now in fact, we could say that a real number 𝑎 is of the form 𝑎 plus zero 𝑖. Zero is indeed a real number. And by its very definition, 𝑎 plus zero 𝑖 is a complex number.

So we have shown that any real number is also a complex number. We can say that the statement “Any real number is also a complex number” is true. It’s important to note though that the opposite statement is not true. We cannot say any complex number is also a real number, since a complex number has a real and an imaginary part. The only way that a complex number can also be a real number is if the imaginary part is zero.