What is the use/need of complex numbers in real life if they are imaginary?
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Electricity consumption is measured in watts (real power). However, the rating of the equipment is measured in kVA (complex power). So, from a numerical standpoint, watts is like your real number component and kVA is your complex number. The imaginary component is called reactive power and measured in kVAR (volt-ampere reactive).
In general, you want your electricity load to require as low reactive power as possible because this means you’re equipment will be cheaper and you are essentially charging the same amount of real power consumption. This property is called power factor, ratio of real power over complex/apparent power. High power factor means your reactive power load is low.
Utility companies incentivise industrial consumers to increase their power factor with discounts and there are actually businesses whose main service is to do exactly that.
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