#include <stdio.h>
#include <math.h>

/* 構造体宣言 */
struct Complex{
    double Real;
    double Imag;
};

struct Complex C_DOUBLE(double a,double b);
struct Complex C_PLUS(struct Complex z1,struct Complex z2);
struct Complex C_MINUS(struct Complex z1,struct Complex z2);
struct Complex C_TIMES(struct Complex z1,struct Complex z2);
struct Complex C_DIVIDED(struct Complex z1,struct Complex z2);
double D_ABS(struct Complex z);
struct Complex C_CONJ(struct Complex z);
struct Complex C_SQRT(struct Complex z);
struct Complex C_EXP(struct Complex z);
struct Complex C_COS(struct Complex z);
struct Complex C_SIN(struct Complex z);
struct Complex C_COSH(struct Complex z);
struct Complex C_SINH(struct Complex z);
/*----------------------------------------------------------------------*/

/**********************************************/
/* 複素数計算のための構造体宣言と関数定義開始 */
/**********************************************/
/* 定義済み関数 */
/* za=C_DOUBLE(a,b)   ：複素数実数部と虚数部への数値の代入（Re(z)=a，Im(z)=b）*/
/* za=C_PLUS(z1,z2)   ：加算（za=z1+z2）                  */
/* za=C_MINUS(z1,z2)  ：減算（za=z1-z2）                  */
/* za=C_TIMES(z1,z2)  ：乗算（za=z1*z2）                  */
/* za=C_DIVIDED(z1,z2)：除算（za=z1/z2）                  */
/* da=D_ABS(z)        ：絶対値（da=sqrt(Re(z)^2+Im(z)^2)）*/
/* za=C_CONJ(z)       ：共役複素数（z=a+ib→za=a-ib）     */
/* za=C_SQRT(z)       ：平方根（za=sqrt(z)）              */
/* za=C_EXP(z)        ：exp関数（za=exp(z)）              */
/* za=C_COS(z)        ：cos関数（za=cos(z)）              */
/* za=C_SIN(z)        ：sin関数（za=sin(z)）              */
/* za=C_COSH(z)       ：cosh関数（za=cosh(z)）            */
/* za=C_SINH(z)       ：sinh関数（za=sinh(z)）            */
/*----------------------------------------------------------------------*/

struct Complex C_DOUBLE(double a,double b)
{
    /* 複素数実数部と虚数部への数値の代入 */
    struct Complex zr;
    zr.Real=a;
    zr.Imag=b;
    return zr;
}
/*----------------------------------------------------------------------*/

struct Complex C_PLUS(struct Complex z1,struct Complex z2)
{
    /* 加算 */
    struct Complex zr;
    zr.Real=z1.Real+z2.Real;
    zr.Imag=z1.Imag+z2.Imag;
    return zr;
}
/*----------------------------------------------------------------------*/

struct Complex C_MINUS(struct Complex z1,struct Complex z2)
{
    /* 減算 */
    struct Complex zr;
    zr.Real=z1.Real-z2.Real;
    zr.Imag=z1.Imag-z2.Imag;
    return zr;
}

/*----------------------------------------------------------------------*/
struct Complex C_TIMES(struct Complex z1,struct Complex z2)
{
    /* 乗算 */
    struct Complex zr;
    zr.Real=z1.Real*z2.Real-z1.Imag*z2.Imag;
    zr.Imag=z1.Real*z2.Imag+z2.Real*z1.Imag;
    return zr;
}

/*----------------------------------------------------------------------*/
struct Complex C_DIVIDED(struct Complex z1,struct Complex z2)
{
    /* 除算 */
    struct Complex zr;
    zr.Real=0.0;
    zr.Imag=0.0;
    if(z2.Real==0.0&&z2.Imag==0.0){
        printf("分母が0です！");
        zr.Real=0.0;
        zr.Imag=0.0;
    }else{
        zr.Real=(z1.Real*z2.Real+z1.Imag*z2.Imag)/(z2.Real*z2.Real+z2.Imag*z2.Imag);
        zr.Imag=(z2.Real*z1.Imag-z1.Real*z2.Imag)/(z2.Real*z2.Real+z2.Imag*z2.Imag);
    }
    return zr;
}

/*----------------------------------------------------------------------*/
double D_ABS(struct Complex z)
{
    /* 絶対値 */
    return sqrt(z.Real*z.Real+z.Imag*z.Imag);
}

/*----------------------------------------------------------------------*/
struct Complex C_CONJ(struct Complex z)
{
    /* 共役複素数 */
    struct Complex zr;
    zr.Real=z.Real;
    zr.Imag=-z.Imag;
    return zr;
}

/*----------------------------------------------------------------------*/
struct Complex C_SQRT(struct Complex z)
{
    /* 平方根 */
    struct Complex zr;
    double rr;
    double phi;
    if(z.Real==0.0&&z.Imag==0.0){
        zr.Real=0.0;
        zr.Imag=0.0;
    }else{
        rr=sqrt(z.Real*z.Real+z.Imag*z.Imag);
        phi=acos(z.Real/rr);
        if(z.Imag<0.0)phi=2.0*M_PI-phi; /* phiの範囲を0〜2πとする（acosの戻り値は0〜π） */
        zr.Real=pow(rr,0.5)*cos(0.5*phi);
        zr.Imag=pow(rr,0.5)*sin(0.5*phi);
    }
    return zr;
}

/*----------------------------------------------------------------------*/
struct Complex C_EXP(struct Complex z)
{
    /* EXP関数 */
    struct Complex zr;
    zr.Real=exp(z.Real)*cos(z.Imag);
    zr.Imag=exp(z.Real)*sin(z.Imag);
    return zr;
}

/*----------------------------------------------------------------------*/
struct Complex C_COS(struct Complex z)
{
    /* cos関数 */
    struct Complex zr;
    zr.Real=0.5*(exp(-z.Imag)+exp(z.Imag))*cos(z.Real);
    zr.Imag=0.5*(exp(-z.Imag)-exp(z.Imag))*sin(z.Real);
    return zr;
}

/*----------------------------------------------------------------------*/
struct Complex C_SIN(struct Complex z)
{
    /* sin関数 */
    struct Complex zr;
    zr.Real=0.5*(exp(-z.Imag)+exp(z.Imag))*sin(z.Real);
    zr.Imag=-0.5*(exp(-z.Imag)-exp(z.Imag))*cos(z.Real);
    return zr;
}

/*----------------------------------------------------------------------*/
struct Complex C_COSH(struct Complex z)
{
    /* cosh関数 */
    struct Complex zr;
    zr.Real=0.5*(exp(z.Real)+exp(-z.Real))*cos(z.Imag);
    zr.Imag=0.5*(exp(z.Real)-exp(-z.Real))*sin(z.Imag);
    return zr;
}

/*----------------------------------------------------------------------*/
struct Complex C_SINH(struct Complex z)
{
    /* sinh関数 */
    struct Complex zr;
    zr.Real=0.5*(exp(z.Real)-exp(-z.Real))*cos(z.Imag);
    zr.Imag=0.5*(exp(z.Real)+exp(-z.Real))*sin(z.Imag);
    return zr;
}

/**********************************************/
/* 複素数計算のための構造体宣言と関数定義終了 */
/**********************************************/

/*----------------------------------------------------------------------*/
int main()
{
    struct Complex z,z1,z2,z3,z4;

    /* 虚数計算チェック */

    /* 四則演算 */
    /* (1-i)/(1+i)=-i */
    z1=C_DOUBLE(1,-1);
    z2=C_DOUBLE(1,1);
    z=C_DIVIDED(z1,z2);
    printf("01 %e %e   %e %e\n",z.Real,z.Imag,0.0,-1.0);

    /* i/(1-i)+(1-i)/i=-3/2-1/2*i */
    z1=C_DIVIDED(C_DOUBLE(0,1),C_DOUBLE(1,-1));
    z2=C_DIVIDED(C_DOUBLE(1,-1),C_DOUBLE(0,1));
    z=C_PLUS(z1,z2);
    printf("02 %e %e   %e %e\n",z.Real,z.Imag,-3.0/2.0,-1.0/2.0);

    /* {(3+4*i)/(1-2*i)}^2=-3-4*i */
    z1=C_DIVIDED(C_DOUBLE(3,4),C_DOUBLE(1,-2));
    z=C_TIMES(z1,z1);
    printf("03 %e %e   %e %e\n",z.Real,z.Imag,-3.0,-4.0);

    /* 平方根 */
    /* sqrt(2) */
    z=C_SQRT(C_DOUBLE(2,0));
    printf("04 %e %e   %e %e\n",z.Real,z.Imag,sqrt(2.0),0.0);
    
    /* sqrt(3) */
    z=C_SQRT(C_DOUBLE(3,0));
    printf("05 %e %e   %e %e\n",z.Real,z.Imag,sqrt(3.0),0.0);
    
    /* sqrt(-i)=cos(3/4*pi)+i*sin(3/4*pi) */
    z=C_SQRT(C_DOUBLE(0,-1));
    printf("06 %e %e   %e %e\n",z.Real,z.Imag,cos(3.0/4.0*M_PI),sin(3.0/4.0*M_PI));

    /* exp関数 */
    /* e^(i*z)=cos(z)+i*sin(z) */
    z=C_DOUBLE(2.5,-7.3);
    z1=C_EXP(C_TIMES(C_DOUBLE(0,1),z));
    z2=C_PLUS(C_COS(z),C_TIMES(C_DOUBLE(0,1),C_SIN(z)));
    printf("07 %e %e   %e %e\n",z1.Real,z1.Imag,z2.Real,z2.Imag);

    /* 三角関数 */
    /* sin(z)^2+cos(z)^2=1 */
    z=C_DOUBLE(1.0,2.0);
    z1=C_PLUS(C_TIMES(C_SIN(z),C_SIN(z)),C_TIMES(C_COS(z),C_COS(z)));
    printf("08 %e %e   %e %e\n",z1.Real,z1.Imag,1.0,0.0);

    /* sin(z1+z2)=sin(z1)*cos(z2)+cos(z1)*sin(z2) */
    z1=C_DOUBLE(1.7,-3.6);
    z2=C_DOUBLE(200.0,-0.3);
    z3=C_SIN(C_PLUS(z1,z2));
    z4=C_PLUS(C_TIMES(C_SIN(z1),C_COS(z2)),C_TIMES(C_COS(z1),C_SIN(z2)));
    printf("09 %e %e   %e %e\n",z3.Real,z3.Imag,z4.Real,z4.Imag);

    /* cos(z1+z2)=cos(z1)*cos(z2)-sin(z1)*sin(z2) */
    z1=C_DOUBLE(1.7,-3.6);
    z2=C_DOUBLE(200.0,-0.3);
    z3=C_COS(C_PLUS(z1,z2));
    z4=C_MINUS(C_TIMES(C_COS(z1),C_COS(z2)),C_TIMES(C_SIN(z1),C_SIN(z2)));
    printf("10 %e %e   %e %e\n",z3.Real,z3.Imag,z4.Real,z4.Imag);

    /* 双曲線関数 */
    /* cosh(z)=1/2*(e^z+e^(-z)) */
    z=C_DOUBLE(1.7,-3.6);
    z1=C_COSH(z);
    z2=C_EXP(z);
    z3=C_EXP(C_TIMES(C_DOUBLE(-1,0),z));
    z4=C_TIMES(C_DOUBLE(0.5,0),C_PLUS(z2,z3));
    printf("11 %e %e   %e %e\n",z1.Real,z1.Imag,z4.Real,z4.Imag);

    /* sinh(z)=1/2*(e^z-e^(-z)) */
    z=C_DOUBLE(1.7,-3.6);
    z1=C_SINH(z);
    z2=C_EXP(z);
    z3=C_EXP(C_TIMES(C_DOUBLE(-1,0),z));
    z4=C_TIMES(C_DOUBLE(0.5,0),C_MINUS(z2,z3));
    printf("12 %e %e   %e %e\n",z1.Real,z1.Imag,z4.Real,z4.Imag);

    /* cosh(z)^2-sinh(z)^2=1 */
    z=C_DOUBLE(1.7,-3.6);
    z1=C_COSH(z);
    z2=C_SINH(z);
    z3=C_MINUS(C_TIMES(z1,z1),C_TIMES(z2,z2));
    printf("13 %e %e   %e %e\n",z3.Real,z3.Imag,1.0,0.0);

    /* sinh(i*z)=i*sin(z) */
    z=C_DOUBLE(1.7,-3.6);
    z1=C_SINH(C_TIMES(C_DOUBLE(0,1),z));
    z2=C_TIMES(C_DOUBLE(0,1),C_SIN(z));
    printf("14 %e %e   %e %e\n",z1.Real,z1.Imag,z2.Real,z2.Imag);

    /* cosh(i*z)=cos(z) */
    z=C_DOUBLE(1.7,-3.6);
    z1=C_COSH(C_TIMES(C_DOUBLE(0,1),z));
    z2=C_COS(z);
    printf("15 %e %e   %e %e\n",z1.Real,z1.Imag,z2.Real,z2.Imag);

    /* sin(i*z)=i*sinh(z) */
    z=C_DOUBLE(1.7,-3.6);
    z1=C_SIN(C_TIMES(C_DOUBLE(0,1),z));
    z2=C_TIMES(C_DOUBLE(0,1),C_SINH(z));
    printf("16 %e %e   %e %e\n",z1.Real,z1.Imag,z2.Real,z2.Imag);

    /* cos(i*z)=cosh(z) */
    z=C_DOUBLE(1.7,-3.6);
    z1=C_COS(C_TIMES(C_DOUBLE(0,1),z));
    z2=C_COSH(z);
    printf("17 %e %e   %e %e\n",z1.Real,z1.Imag,z2.Real,z2.Imag);

    /* sinh(z1+z2)=sinh(z1)*cosh(z2)+cosh(z1)*sinh(z2) */
    z1=C_DOUBLE(1.7,-3.6);
    z2=C_DOUBLE(2.0,-0.3);
    z3=C_SINH(C_PLUS(z1,z2));
    z4=C_PLUS(C_TIMES(C_SINH(z1),C_COSH(z2)),C_TIMES(C_COSH(z1),C_SINH(z2)));
    printf("18 %e %e   %e %e\n",z3.Real,z3.Imag,z4.Real,z4.Imag);

    /* cosh(z1+z2)=cosh(z1)*cosh(z2)+sinh(z1)*sinh(z2) */
    z1=C_DOUBLE(1.7,-3.6);
    z2=C_DOUBLE(2.0,-0.3);
    z3=C_COSH(C_PLUS(z1,z2));
    z4=C_PLUS(C_TIMES(C_COSH(z1),C_COSH(z2)),C_TIMES(C_SINH(z1),C_SINH(z2)));
    printf("19 %e %e   %e %e\n",z3.Real,z3.Imag,z4.Real,z4.Imag);

    printf("リターンキーを押してください");
    getchar();
    return 0;
}
/*----------------------------------------------------------------------*/