Option Explicit On
Option Strict On
Public Class Form1
    '***********************************************************
    '複素数計算のための構造体宣言とFunctionプロシージャ開始
    '***********************************************************
    '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)）

    Private Structure Complex
        '構造体宣言
        Dim Real As Double
        Dim Imag As Double
    End Structure

    Private Function C_DOUBLE(ByVal a As Double, ByVal b As Double) As Complex
        '複素数実数部と虚数部への数値の代入
        C_DOUBLE.Real = a
        C_DOUBLE.Imag = b
    End Function

    Private Function C_PLUS(ByVal z1 As Complex, ByVal z2 As Complex) As Complex
        '加算
        C_PLUS.Real = z1.Real + z2.Real
        C_PLUS.Imag = z1.Imag + z2.Imag
    End Function

    Private Function C_MINUS(ByVal z1 As Complex, ByVal z2 As Complex) As Complex
        '減算
        C_MINUS.Real = z1.Real - z2.Real
        C_MINUS.Imag = z1.Imag - z2.Imag
    End Function

    Private Function C_TIMES(ByVal z1 As Complex, ByVal z2 As Complex) As Complex
        '乗算
        C_TIMES.Real = z1.Real * z2.Real - z1.Imag * z2.Imag
        C_TIMES.Imag = z1.Real * z2.Imag + z2.Real * z1.Imag
    End Function

    Private Function C_DIVIDED(ByVal z1 As Complex, ByVal z2 As Complex) As Complex
        '除算
        If z2.Real = 0.0 And z2.Imag = 0.0 Then
            MessageBox.Show("分母が0です！")
            Me.Close()
        Else
            C_DIVIDED.Real = (z1.Real * z2.Real + z1.Imag * z2.Imag) / (z2.Real ^ 2 + z2.Imag ^ 2)
            C_DIVIDED.Imag = (z2.Real * z1.Imag - z1.Real * z2.Imag) / (z2.Real ^ 2 + z2.Imag ^ 2)
        End If
    End Function

    Private Function D_ABS(ByVal z As Complex) As Double
        '絶対値
        D_ABS = Math.Sqrt(z.Real ^ 2 + z.Imag ^ 2)
    End Function

    Private Function C_CONJ(ByVal z As Complex) As Complex
        '共役複素数
        C_CONJ.Real = z.Real
        C_CONJ.Imag = -z.Imag
    End Function

    Private Function C_SQRT(ByVal z As Complex) As Complex
        '平方根
        If z.Real = 0.0 And z.Imag = 0.0 Then
            C_SQRT.Real = 0.0
            C_SQRT.Imag = 0.0
        Else
            Dim rr As Double
            Dim phi As Double
            rr = Math.Sqrt(z.Real ^ 2 + z.Imag ^ 2)
            phi = Math.Acos(z.Real / rr)
            If z.Imag < 0.0 Then phi = 2.0 * Math.PI - phi 'phiの範囲を0〜2πとする（acosの戻り値は0〜π）
            C_SQRT.Real = rr ^ (0.5) * Math.Cos(0.5 * phi)
            C_SQRT.Imag = rr ^ (0.5) * Math.Sin(0.5 * phi)
        End If
    End Function

    Private Function C_EXP(ByVal z As Complex) As Complex
        'EXP関数
        C_EXP.Real = Math.Exp(z.Real) * Math.Cos(z.Imag)
        C_EXP.Imag = Math.Exp(z.Real) * Math.Sin(z.Imag)
    End Function

    Private Function C_COS(ByVal z As Complex) As Complex
        'cos関数
        C_COS.Real = 0.5 * (Math.Exp(-z.Imag) + Math.Exp(z.Imag)) * Math.Cos(z.Real)
        C_COS.Imag = 0.5 * (Math.Exp(-z.Imag) - Math.Exp(z.Imag)) * Math.Sin(z.Real)
    End Function

    Private Function C_SIN(ByVal z As Complex) As Complex
        'sin関数
        C_SIN.Real = 0.5 * (Math.Exp(-z.Imag) + Math.Exp(z.Imag)) * Math.Sin(z.Real)
        C_SIN.Imag = -0.5 * (Math.Exp(-z.Imag) - Math.Exp(z.Imag)) * Math.Cos(z.Real)
    End Function

    Private Function C_COSH(ByVal z As Complex) As Complex
        'cosh関数
        C_COSH.Real = 0.5 * (Math.Exp(z.Real) + Math.Exp(-z.Real)) * Math.Cos(z.Imag)
        C_COSH.Imag = 0.5 * (Math.Exp(z.Real) - Math.Exp(-z.Real)) * Math.Sin(z.Imag)
    End Function

    Private Function C_SINH(ByVal z As Complex) As Complex
        'sinh関数
        C_SINH.Real = 0.5 * (Math.Exp(z.Real) - Math.Exp(-z.Real)) * Math.Cos(z.Imag)
        C_SINH.Imag = 0.5 * (Math.Exp(z.Real) + Math.Exp(-z.Real)) * Math.Sin(z.Imag)
    End Function
    '***********************************************************
    '複素数計算のための構造体宣言とFunctionプロシージャ終了
    '***********************************************************

    Private Sub Button1_Click(ByVal sender As System.Object, ByVal e As System.EventArgs) Handles Button1.Click
        Dim z As Complex
        Dim z1 As Complex
        Dim z2 As Complex
        Dim z3 As Complex
        Dim z4 As Complex

        '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)
        Console.WriteLine(z.Real.ToString & "  " & z.Imag.ToString)

        '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)
        Console.WriteLine(z.Real.ToString & "  " & z.Imag.ToString)

        '{(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)
        Console.WriteLine(z.Real.ToString & "  " & z.Imag.ToString)

        '平方根
        'sqrt(2)
        z = C_SQRT(C_DOUBLE(2, 0))
        Console.WriteLine(z.Real.ToString & "  " & z.Imag.ToString)
        'sqrt(3)
        z = C_SQRT(C_DOUBLE(3, 0))
        Console.WriteLine(z.Real.ToString & "  " & z.Imag.ToString)
        'sqrt(-i)=cos(3/4*pi)+i*sin(3/4*pi)
        z = C_SQRT(C_DOUBLE(0, -1))
        Console.WriteLine(z.Real.ToString & "  " & z.Imag.ToString & "  " & Math.Cos(3 / 4 * Math.PI).ToString & "  " & Math.Sin(3 / 4 * Math.PI).ToString)

        '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)))
        Console.WriteLine(z1.Real.ToString & "  " & z1.Imag.ToString & "  " & z2.Real.ToString & "  " & z2.Imag.ToString)

        '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)))
        Console.WriteLine(z1.Real.ToString & "  " & z1.Imag.ToString)

        '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)))
        Console.WriteLine(z3.Real.ToString & "  " & z3.Imag.ToString & "  " & z4.Real.ToString & "  " & z4.Imag.ToString)

        '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)))
        Console.WriteLine(z3.Real.ToString & "  " & z3.Imag.ToString & "  " & z4.Real.ToString & "  " & z4.Imag.ToString)

        '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))
        Console.WriteLine(z1.Real.ToString & "  " & z1.Imag.ToString & "  " & z4.Real.ToString & "  " & z4.Imag.ToString)

        '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))
        Console.WriteLine(z1.Real.ToString & "  " & z1.Imag.ToString & "  " & z4.Real.ToString & "  " & z4.Imag.ToString)

        '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))
        Console.WriteLine(z3.Real.ToString & "  " & z3.Imag.ToString)

        '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))
        Console.WriteLine(z1.Real.ToString & "  " & z1.Imag.ToString & "  " & z2.Real.ToString & "  " & z2.Imag.ToString)

        '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)
        Console.WriteLine(z1.Real.ToString & "  " & z1.Imag.ToString & "  " & z2.Real.ToString & "  " & z2.Imag.ToString)

        '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))
        Console.WriteLine(z1.Real.ToString & "  " & z1.Imag.ToString & "  " & z2.Real.ToString & "  " & z2.Imag.ToString)

        '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)
        Console.WriteLine(z1.Real.ToString & "  " & z1.Imag.ToString & "  " & z2.Real.ToString & "  " & z2.Imag.ToString)

        '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)))
        Console.WriteLine(z3.Real.ToString & "  " & z3.Imag.ToString & "  " & z4.Real.ToString & "  " & z4.Imag.ToString)

        '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)))
        Console.WriteLine(z3.Real.ToString & "  " & z3.Imag.ToString & "  " & z4.Real.ToString & "  " & z4.Imag.ToString)

    End Sub

End Class