Eli5 Why do we need complex numbers in real life?
In: 11
Why do we need negative numbers? Will you ever have -3 cows?
I had 5 cows, 3 died, then I got 4 more, then 5 died again.
The caveman would: 5-3= 2 -> 2+4=6 -> 6-5=1
We however: 5 – 8 + 4 = -3+4=1
That -3 cows would make the caveman lose his shit. I had 5 lost 8 and got 4. We understand that this is useful. We get more freedom in doing calculations. Nobody cares that during the calculation -3 cows just show up.
Same with complex numbers. They give you more freedom during calculations. It may seem that problems are more complicated with complex, but its usually the opposite.
Or think like this: it would be hard to do algebra if we don’t allow negatives. In that case subtraction isn’t commutative. So moving terms left and right is a problem, until you say that subtraction is addition with negative numbers. Then you can shuffle things around easily.
Complex numbers (and theorems of complex analysis) makes many calculations easier.
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