Answered

2022-01-17

If the equation ${(z+1)}^{7}+{z}^{7}=0$ has roots $z}_{1},{z}_{2},\cdots {z}_{7$

then what is the value of$\sum _{r=1}^{7}\mathbb{R}\left({Z}_{r}\right)?$

then what is the value of

Answer & Explanation

nick1337

Expert

2022-01-17Added 573 answers

Step 1

I would choose a different approach, saving some labour:

The polynomial:

And may also be written as:

The sum of the roots of the monomial

The sum of the roots of

star233

Expert

2022-01-17Added 238 answers

Step 1

You can observe that z=0 is not a solution, so the equation can be rewritten as

Hence we get

for

Write

and therefore

and we obtain

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