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Complex Roots Unleashed (Posted on 2024-04-23)

A complex number a≠-1 is the root of an equation x³+1=0.

Find 1+2a+3a²+4a³+5a⁴.

No Solution Yet Submitted by Danish Ahmed Khan

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computer solution

| Comment 4 of 7 |

syms x

s=solve(x^3+1==0)

for a=[s(2) s(3)]

simplify(1+2*a+3*a^2+4*a^3+5*a^4)

end

finds

s =

-1

1/2 - (3^(1/2)*1i)/2

(3^(1/2)*1i)/2 + 1/2

ans =

-6

ans =

-6

The answer is 1+2*a+3*a^2+4*a^3+5*a^4 = -6

Posted by Charlie on 2024-04-23 11:14:35

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