.NET 4.0 New Feature - Complex
.NET 4.0新增了Complex類別，位於System.Numerics.dll組件內的System.Numerics中，可用來描述與處理複數資料，具備數值比對、算術運算、其它數值運算 、與三角運算等複數資料運算的能力。
使用上需先加入System.Numerics.dll組件參考
並將System.Numerics命名空間匯入
加入了參考與命名空間後，我們就可以開始來使用Complex型別了。首先，我們必需建立Complex型別變數。
Complex型別變數有三種建立方式，一種是透過Complex的建構子將數值的實數部份與虛數部份帶入建構子建構。
一種則是先宣告出Complex變數，在將值塞入後使用。
這邊需注意到的是，由於Complex是用以表示複數，而複數是由實數部份與虛數部份所構成，因此採用這種直接把值塞入的作法，只能設定到複數的實數部份，虛數部份會被設定為0。
最後一種則是透過Complex.FromPolarCoordinates靜態方法來從極座標建立Complex變數
建立完後可對其做些運算處理，這邊不一一詳述，自行參閱下方整理的範例：
Module Module1
Sub Main()
ShowDetail("Complex.Zero", Complex.Zero)
ShowDetail("Complex.One", Complex.One)
Dim c1 As New Complex(1, 2)
Dim c2 As New Complex(3, 4)
ShowDetail("C1", c1)
ShowDetail("C2", c2)
'Complex +-*/
Console.WriteLine("{0} + {1} = {2}", c1, c2, c1 + c2)
Console.WriteLine("{0} - {1} = {2}", c1, c2, c1 - c2)
Console.WriteLine("{0} * {1} = {2}", c1, c2, c1 * c2)
Console.WriteLine("{0} / {1} = {2}", c1, c2, c1 / c2)
Console.WriteLine()
Console.WriteLine("Complex.Add({0}, {1}) = {2}", c1, c2, Complex.Add(c1, c2))
Console.WriteLine("Complex.Subtract({0}, {1}) = {2}", c1, c2, Complex.Subtract(c1, c2))
Console.WriteLine("Complex.Multiply({0}, {1}) = {2}", c1, c2, Complex.Multiply(c1, c2))
Console.WriteLine("Complex.Divide({0}, {1}) = {2}", c1, c2, Complex.Divide(c1, c2))
Console.WriteLine()
'Other Complex operation
Console.WriteLine("Complex.Divide({0}) = {1}", c1, Complex.Conjugate(c1))
Console.WriteLine("Complex.Abs({0}) = {1}", c1, Complex.Abs(c1))
Console.WriteLine("Complex.Negate({0}) = {1}", c1, Complex.Negate(c1))
Console.WriteLine("Complex.Pow({0}, 2) = {1}", c1, Complex.Pow(c1, 2))
Console.WriteLine("Complex.Pow({0}, {1}) = {2}", c1, c2, Complex.Pow(c1, c2))
Console.WriteLine("Complex.Sqrt({0}) = {1}", c1, Complex.Sqrt(c1))
Console.WriteLine("Complex.Reciprocal({0}) = {1}", c1, Complex.Reciprocal(c1))
Console.WriteLine("Complex.Log({0}) = {1}", c1, Complex.Log(c1))
Console.WriteLine("Complex.Log10({0}) = {1}", c1, Complex.Log10(c1))
Console.WriteLine("Complex.exp({0}) = {1}", c1, Complex.Exp(c1))
Console.WriteLine()
Console.WriteLine("Complex.Sin({0}) = {1}", c1, Complex.Sin(c1))
Console.WriteLine("Complex.Sinh({0}) = {1}", c1, Complex.Sinh(c1))
Console.WriteLine("Complex.Cos({0}) = {1}", c1, Complex.Cos(c1))
Console.WriteLine("Complex.Cosh({0}) = {1}", c1, Complex.Cosh(c1))
Console.WriteLine("Complex.Tan({0}) = {1}", c1, Complex.Tan(c1))
Console.WriteLine("Complex.Tanh({0}) = {1}", c1, Complex.Tanh(c1))
Console.WriteLine("Complex.Asin({0}) = {1}", c1, Complex.Asin(c1))
Console.WriteLine("Complex.Acos({0}) = {1}", c1, Complex.Acos(c1))
Console.WriteLine("Complex.Atan({0}) = {1}", c1, Complex.Atan(c1))
End Sub
Private Sub ShowDetail(ByVal varName As String, ByVal c As Complex)
Console.WriteLine("{0}: {1}", varName, c)
ShowDetail(c)
Console.WriteLine()
End Sub
Private Sub ShowDetail(ByVal c As Complex)
Console.WriteLine("Real: {0}", c.Real)
Console.WriteLine("Imaginary: {0}", c.Imaginary)
Console.WriteLine("Phase: {0}", c.Phase)
Console.WriteLine("Magnitude: {0}", c.Magnitude)
End Sub
End Module
運行結果如下：
Real: 0
Imaginary: 0
Phase: 0
Magnitude: 0
Complex.One: (1, 0)
Real: 1
Imaginary: 0
Phase: 0
Magnitude: 1
C1: (1, 2)
Real: 1
Imaginary: 2
Phase: 1.10714871779409
Magnitude: 2.23606797749979
C2: (3, 4)
Real: 3
Imaginary: 4
Phase: 0.927295218001612
Magnitude: 5
(1, 2) + (3, 4) = (4, 6)
(1, 2) - (3, 4) = (-2, -2)
(1, 2) * (3, 4) = (-5, 10)
(1, 2) / (3, 4) = (0.44, 0.08)
Complex.Add((1, 2), (3, 4)) = (4, 6)
Complex.Subtract((1, 2), (3, 4)) = (-2, -2)
Complex.Multiply((1, 2), (3, 4)) = (-5, 10)
Complex.Divide((1, 2), (3, 4)) = (0.44, 0.08)
Complex.Divide((1, 2)) = (1, -2)
Complex.Abs((1, 2)) = 2.23606797749979
Complex.Negate((1, 2)) = (-1, -2)
Complex.Pow((1, 2), 2) = (-3, 4)
Complex.Pow((1, 2), (3, 4)) = (0.129009594074467, 0.0339240929051702)
Complex.Sqrt((1, 2)) = (1.27201964951407, 0.786151377757423)
Complex.Reciprocal((1, 2)) = (0.2, -0.4)
Complex.Log((1, 2)) = (0.80471895621705, 1.10714871779409)
Complex.Log10((1, 2)) = (0.349485002168008, 0.480828578784232)
Complex.exp((1, 2)) = (-1.13120438375681, 2.47172667200482)
Complex.Sin((1, 2)) = (3.16577851321617, 1.95960104142161)
Complex.Sinh((1, 2)) = (-0.489056259041294, 1.40311925062204)
Complex.Cos((1, 2)) = (2.03272300701967, -3.0518977991518)
Complex.Cosh((1, 2)) = (-0.64214812471552, 1.06860742138278)
Complex.Tan((1, 2)) = (0.0338128260798967, 1.01479361614663)
Complex.Tanh((1, 2)) = (1.16673625724092, -0.243458201185725)
Complex.Asin((1, 2)) = (0.427078586392476, 1.528570919481)
Complex.Acos((1, 2)) = (1.14371774040242, -1.528570919481)
Complex.Atan((1, 2)) = (1.33897252229449, 0.402359478108525)