What is the use/need of complex numbers in real life if they are imaginary?
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They are no more or less imaginary than regular (“real”) numbers, that was just a bad naming choice. All that it means is you can’t mix them with regular numbers. Like you can’t add 3 real + 2 imaginary = 5 something. 3 + 2i must always remain separate components. The real number and the complex number are in different mathematical dimensions.
Because of this property, complex numbers are useful when calculating two properties that are mathematically related, but cannot be substituted for one another – like electricity and magnetism. You can have 5 electricity and 3 magnetism from a wire (which could be represented as 5+3i), but saying you have 8 electromagnetism is invalid. You could also just write the maths with electricity and magnetism as separate numbers, but it hides the fact that when one changes so does the other.
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