Finding The Complex Roots Of A Polynomial

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How does one find complex roots of a polynomial? Can you please keep the explanation simple, because I am still a high school student? Please try to keep the answer at the level of a high school pre-calculus student. Also, can you please explain why your method works; don't just give me a method to find imaginary/complex roots of a polynomial. Thank you!

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It’s a very complicated question actually. There are formulas to find roots for polynomials of degree 3&4, (in this case it’s very similar to polynomials of degree 2), but no formulas for polynomials of degree higher than 5. Yet maybe someone who is much better at mathematics can explain it in a simple way!