Undergrad Scalar quantities and complex numbers

[topito2]

I was taught a scalar is a quantity that consists of a number (positive or negative) and it might include a measuring unit, e.g. 6, 5 kg, -900 J, etc. I was wondering if complex numbers like 3 + 7j (where j is the square root of minus 1) can be considered scalar quantities too, or is it that only real numbers (that might include measuring units) can be considered scalars?

 

[Khashishi]

Complex numbers are considered scalars. Although complex numbers can be thought of as a magnitude and direction in the 2D number plane, the number plane is a mathematical space and not a physical space like horizontal and vertical.

 

[fresh_42]

I was taught a scalar is a quantity that consists of a number (positive or negative) and it might include a measuring unit, e.g. 6, 5 kg, -900 J, etc. I was wondering if complex numbers like 3 + 7j (where j is the square root of minus 1) can be considered scalar quantities too, or is it that only real numbers (that might include measuring units) can be considered scalars?

Scalars are numbers, rationals, reals, complex or even quaternions. Units are not part of them! A unit is a special measure of a dimension like length or weight. Scalars are dimensionless.

 

[topito2]

Thank you so much for the speedy reply, guys! BTW, could you please provide any reference (book or website) I could check to dig a little bit more on the subject?

 

[fresh_42]

Thank you so much for the speedy reply, guys! BTW, could you please provide any reference (book or website) I could check to dig a little bit more on the subject?

Can you tell which direction?
Scalars as numbers? Which? Scalars as part of vector spaces or algebras? Scalar fields? Scalars as opposing vectors?
In the end they are simply numbers. Which, depends on what for. Or which role they play in certain contexts.