Complex numbers are magnificent, the pinnacle of number systems. They enjoy all the same properties as real numbers—you can add and subtract them, multiply and divide them—but they are better than real numbers because they always have roots.
You can take the square root or cube root or any root of a complex number, and the result will still be a complex number. Better yet, a grand statement called the fundamental theorem of algebra says that the roots of any polynomial are always complex numbers.
In that sense they’re the end of the quest, the holy grail.
The universe of numbers need never expand again. Complex numbers are the culmination of the journey that began with 1.
From: The Joy of x: A Guided Tour of Math, from One to Infinity by Strogatz, Steven