複數類n次方原理以及C#代碼實現

完整代碼下載https://download.csdn.net/download/u012737193/10359608

我們這裏將複數類表示爲complx = real + imag * i

那麼要如何計算complex ^ n呢，這裏的n是double類型，可以是任何數

首先進行如下轉換

因此complex = r *(cos(mu)+ sin(mu)*i) = r*(e ^ (mu * i))（歐拉公式）

因此complex ^ n = (r^ n) * (e ^ (mu * n * i))

因此r2 = r ^ n ，mu2 = mu * n

real2 = r2 * cos(mu2) = (r ^ n) *cos(mu *n)

imag2 = r2 * cos(mu2) = (r ^ n) *sin(mu *n)

complex2 = complex ^ n = real2 + imag2 * i

至此得到結果complex類C#的實現如下

  classcomplex

    {

        double imag_;

double real_;

        double r()

        {

            return  Math.Sqrt(Math.Pow(imag_, 2) + Math.Pow(real_, 2));

        }

        double mu()

        {

            returnMath.Atan2(imag_, real_);

        }

        public complex()

        {

            this.imag_ = 0;

            this.real_ = 0;

        }

        public complex(double real,double imag)

        {

            this.imag_ = imag;

            this.real_ = real;

        }

        publicdouble imag()

        {

            return imag_;

        }

        publicdouble real()

        {

            return real_;

        }

        publiccomplex Pow(double comp)

        {

            double ther = r();

            double sita = mu();

            double R = Math.Pow(ther, comp) * Math.Cos(comp * sita);

            double I = Math.Pow(ther, comp) * Math.Sin(comp * sita);

            real_ = R;

            imag_ = I;

            return this;

        }

        //^的重載

        public static complex operator ^(complex z1, double z2)

        {

            return (z1.Pow(z2));

        }

    }