Root of unity problem for wiki

Algebra Level 2

Let zz be a 7th7^\text{th} root of unity. In other words, zz is a complex number that satisfies the equation z7=1z^7 = 1.

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

Give your answer to 3 decimal places.

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