What is the use/need of complex numbers in real life if they are imaginary?
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In electricity calculations, it is possible to depict capacitors and coils to have imaginary and negative imaginary resistances. This is called impedance.
A system could have an impedance of 13+4j Ohm which means it is somewhat capacitive. (in electricity we use j instead of i to avoid confusion with current, which is also depicted as i).
A capacitive or inductive system will also modify the relationship between current and potential, which can also be depicted as an imaginary number.
It’s a long time since I did this, but that’s the gist of it. It makes electrical calculations significantly easier by using complex numbers instead of regular numbers.
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