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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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re: Another way

| Comment 3 of 7 |

(In reply to Another way by Larry)

I like the first half, but we don't need to get into the nitty-gritty introducing the complex roots.

Starting from 3(a^2-a-1).

Factor a^3+1=0 into (a+1)(a^2-a+1)=0. Since we are given a!=-1 then a^2-a+1=0.

Now 3(a^2-a-1)

= 3((a^2-a+1)-2)

= 3(0-2) = -6.

Posted by Brian Smith on 2024-04-23 10:48:27

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