# Root of unity problem for wiki

Algebra Level 4

Let $$z$$ be a $$7^\text{th}$$ root of unity. In other words, $$z$$ is a complex number that satisfies the equation $$z^7 = 1$$.

If $$z=a+bi$$, where $$a$$ and $$b$$ are real numbers, then what is the maximum value of $$a+b$$?

Give your answer to 3 decimal places.

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