and also ELI16 what a an imaginary number is and how it works in real life
In: Mathematics
On a normal numbering you have 1 2 3 4… in one direction and -1 -2 -3 -4… in the other direction.
The rules with multiplying negative numbers are as follows:
– negative x negative = positive
– positive x negative = negative
– positive x negative = positive
Now this makes a lot of sense with not much effort to picture if you’re using that numberline. Multiplying by a negative makes you switch direction on the line.
With this logic we can say that if you square a negative, you will always get a positive number. Because negative x negative is always positive. But this brings up a point:
Squaring a number multiplies it by itself. Therefore I must always be doing either negative x negative or positive x positive. So any negative number squared becomes positive. If that is the case: WHAT HAPPENS WHEN WE LOOK FOR THE SQUARE ROOT OF A NEGATIVE?
There is no rule of nature that says there can’t be a square root of a negative number, but by the rules of our mathematical model, one cannot exist. So mathematicians invented one. Put another numbering over than first one, perpendicular and crossing at 0. We have now invented an imaginary numberline. Except instead of going 1,2,3,4… we go i1,i2,i3,i4. Or -i1,-i2,-i3,-i4…
Square root your negative i numbers and we get j1,j2,j3,j4…
What you might notice if you’ve been drawing this or visualising it is we now have effectively another dimension to maths. Further than this wasn’t covered by my brief course on further maths but I recommend looking into it further if you’re interested. Iirc, Veritasium has a decent video on it.
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