Imaginary and complex numbers become a little easier to understand if you think of the complex plane as a Cartesian grid, with real numbers as the X values and imaginary numbers as the y values
< ( theodore, old fellow, have you heard of the vector mathematics? )
( utterly preposterous, geoff! numbers cannot have two dimensions! ) >
< ( I agree heartily! we shall never use vector mathematics as long as we live! )
( oh dear, this problem would really be solvable if numbers had two dimensions. ) >
< ( well—that’s—but… aha! that’s not really two dimensions! it’s just number a added to number b, with b multiplied by florb! )
( florb? ) >
< ( it’s an undefined thingy that has no numerical equivalent, so a and b can never be combined, if you multiply b by it. )
( brilliant! now we can pretend we’re not using the vector (a,b), write it like a + b * florb, and no one will suspect we stooped to using vector mathematics! ) >
< ( we mathemeticians are pretty brilliant, aren’t we? )
I’ve never been a fan of that notation. It’s confusing and misleading. If zⁿ = -1 has n solutions, why pick an arbitrary one and designate it as theⁿ√(-1)? Indices (z₁ = i, z₂ = -i) and set notation (z ∈ {-i, i}) both feel like better choices for what you’re trying to convey.
Now that that’s out of my system, on to the important things. Scoots looks incredibly adorable in this picture.
Applebloom: ah don’t get it… ooohhh, now I get- head explodes
Edited
( utterly preposterous, geoff! numbers cannot have two dimensions! ) >
< ( I agree heartily! we shall never use vector mathematics as long as we live! )
( oh dear, this problem would really be solvable if numbers had two dimensions. ) >
< ( well—that’s—but… aha! that’s not really two dimensions! it’s just number a added to number b, with b multiplied by florb! )
( florb? ) >
< ( it’s an undefined thingy that has no numerical equivalent, so a and b can never be combined, if you multiply b by it. )
( brilliant! now we can pretend we’re not using the vector (a,b), write it like a + b * florb, and no one will suspect we stooped to using vector mathematics! ) >
< ( we mathemeticians are pretty brilliant, aren’t we? )
Edited
zⁿ = -1
hasn
solutions, why pick an arbitrary one and designate it as theⁿ√(-1)
? Indices (z₁ = i, z₂ = -i
) and set notation (z ∈ {-i, i}
) both feel like better choices for what you’re trying to convey.Now that that’s out of my system, on to the important things. Scoots looks incredibly adorable in this picture.
As real as her ability to reach that high with her wings.