Eli5: in complex numbers, what is the meaning of adding a “+b*i” part? It looks to me similar to ‘normal’ coordinates (+b*y), but with another name. I understand that the meaning of i as the square root of a negative makes it different but could never understand how so.

Question

We were told about complex numbers, and did the algebra by solving problems with the general form of “a*n + b*i”. It does not really behave differently than standard algebra, it seems. What am I missing in the intention or meaning of the “i” part?

In: Mathematics

Answer 1

i isn’t a variable, it’s a constant.

a+bi is three constants. a+by is two constants and a variable.

y^2 is just that, y^2, it doesn’t get simpler and it can never turn into an x. i^2 is just -1.

The algebra (symbol manipulation) is the same but the math meaning is totally different.