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.
