设 z = a+bi;z+1/z = a+bi + 1/(a+bi);= a+bi + (a-bi)/(a² + b²);= a+a/(a² + b²) + ((b-b/(a² + b²))i ;∵ z+1/z 是实数;∴ (b-b/(a² + b²)) = 0;∴ a²+b² = 1...