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Let zzz be a 7th7^\text{th}7th root of unity. In other words, zzz is a complex number that satisfies the equation z7=1z^7 = 1z7=1.
If z=a+biz=a+biz=a+bi, where aaa and bbb are real numbers, then what is the maximum value of a+b?a+b?a+b?
Give your answer to 3 decimal places.
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