how do I find the roots of this equation using only pencil paper and some sort of advanced algorithm: (2+i)*x^9-2*x^5+i*x^3+6*i*x-(8-3*i)=0? can anyone please direct me to or give me the algorithm or algorithms.
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In general, you don't. It can be shown that there exist equations of degree higher than four whose solutions simply cannot be written in terms of algebraic operations (adding, multiplying, roots).
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