You define complex numbers as the reals, i, as usually defined, and their linear combinations using real coefficients, then,
The reals are complex numbers, even if you haven’t fully defined their properties.
If you define complex numbers as the form (a,b) with and a, b are real numbers, then you can say that each real number a is isomorphic with that complex number,
if b=0 once you define their properties.
A complex number can be visually represented as a pair of numbers (a, b) forming a vector on a diagram called an Argand diagram, representing the complex plane.
Of course, (0,1) will be i. You’ll have to define the multiplication rule, etc.
In actual usage, we gloss over the distinction, and real numbers are complex numbers with no imaginary part.
To learn more about the complex number visit:
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