diff --git a/xml/System.Numerics/Complex.xml b/xml/System.Numerics/Complex.xml index 1764baa24bb..73896608c09 100644 --- a/xml/System.Numerics/Complex.xml +++ b/xml/System.Numerics/Complex.xml @@ -314,6 +314,31 @@ + + + Adds a specified number to another specified number, where at least one of them is a complex number, and the other could be a double-precision real number. + + methods allow performing addition operations that involve complex numbers. + + If the method call results in an overflow in either the real or imaginary component, the value of the component is either or . + + Languages that do not support custom operators can use the method to perform addition with complex numbers. + + The methods that receive one double are more efficient than the methods that receive two complex numbers. + +## Examples + + The following example illustrates addition with complex numbers. + + [!code-csharp[System.Numerics.Complex.Add#1](~/samples/snippets/csharp/VS_Snippets_CLR_System/system.numerics.complex.add/cs/add1.cs#1)] + [!code-vb[System.Numerics.Complex.Add#1](~/samples/snippets/visualbasic/VS_Snippets_CLR_System/system.numerics.complex.add/vb/add1.vb#1)] + ]]> + + + @@ -340,11 +365,19 @@ - To be added. - To be added. - To be added. - To be added. - To be added. + The double-precision real value to add. + The complex value to add. + Adds a double-precision real number to a complex number and returns the result. + The sum of and . + + + + @@ -373,11 +406,19 @@ - To be added. - To be added. - To be added. - To be added. - To be added. + The complex value to add. + The double-precision real value to add. + Adds a complex number to a double-precision real number and returns the result. + The sum of and . + + + + @@ -428,18 +469,7 @@ The addition of a complex number, a + bi, and a second complex number, c + di, takes the following form: (a + c) + (b + d)i. - - If the method call results in an overflow in either the real or imaginary component, the value of the component is either or . - - Languages that do not support custom operators can use the method to perform addition with complex numbers. - - - -## Examples - The following example illustrates addition with complex numbers. - - [!code-csharp[System.Numerics.Complex.Add#1](~/samples/snippets/csharp/VS_Snippets_CLR_System/system.numerics.complex.add/cs/add1.cs#1)] - [!code-vb[System.Numerics.Complex.Add#1](~/samples/snippets/visualbasic/VS_Snippets_CLR_System/system.numerics.complex.add/vb/add1.vb#1)] + ]]> @@ -721,6 +751,31 @@ + + + Divides a specified number by another specified number, where at least one of them is a complex number, and the other could be a double-precision real number. + + methods allow performing division operations that involve complex numbers. + + If the calculation of the quotient results in an overflow in either the real or imaginary component, the value of that component is either or . + + The method can be used by languages that do not support custom operators. Its behavior is identical to division using the division operator. + + The methods that receive one double are more efficient than the methods that receive two complex numbers. + +## Examples + The following example divides a complex number by each element in an array of complex numbers. + + [!code-csharp[System.Numerics.Complex.Divide#1](~/samples/snippets/csharp/VS_Snippets_CLR_System/system.numerics.complex.divide/cs/divide1.cs#1)] + [!code-vb[System.Numerics.Complex.Divide#1](~/samples/snippets/visualbasic/VS_Snippets_CLR_System/system.numerics.complex.divide/vb/divide1.vb#1)] + + ]]> + + + @@ -747,11 +802,22 @@ - To be added. - To be added. - To be added. - To be added. - To be added. + The double-precision real number to be divided. + The complex number to divide by. + Divides one double-precision real number by a complex number and returns the result. + The quotient of the division. + + 2 + d2)) + (ad / (c2 + d2)i + + ]]> + + @@ -780,11 +846,22 @@ - To be added. - To be added. - To be added. - To be added. - To be added. + The complex number to be divided. + The double-precision real number to divide by. + Divides one complex number by a double-precision real number and returns the result. + The quotient of the division. + + 2) + (bc / c2)i + + ]]> + + @@ -835,19 +912,7 @@ The division of a complex number, a + bi, by a second complex number, number, c + di, takes the following form: ((ac + bd) / (c2 + d2)) + ((bc - ad) / (c2 + d2)i - - If the calculation of the quotient results in an overflow in either the real or imaginary component, the value of that component is either or . - - The method can be used by languages that do not support custom operators. Its behavior is identical to division using the division operator. - - - -## Examples - The following example divides a complex number by each element in an array of complex numbers. - - [!code-csharp[System.Numerics.Complex.Divide#1](~/samples/snippets/csharp/VS_Snippets_CLR_System/system.numerics.complex.divide/cs/divide1.cs#1)] - [!code-vb[System.Numerics.Complex.Divide#1](~/samples/snippets/visualbasic/VS_Snippets_CLR_System/system.numerics.complex.divide/vb/divide1.vb#1)] - + ]]> @@ -1261,7 +1326,7 @@ System.Numerics.Complex - To be added. + Represents infinity as a complex number. To be added. @@ -1290,9 +1355,9 @@ - To be added. - To be added. - To be added. + A complex number. + Determines whether the specified complex number is finite. + if both, the real and imaginary parts are finite (zero, subnormal or normal); otherwise, . To be added. @@ -1321,9 +1386,9 @@ - To be added. - To be added. - To be added. + A complex number. + Returns a value indicating whether the specified complex number evaluates to infinity. + if either, the real or imaginary part are or ; otherwise, . To be added. @@ -1352,9 +1417,9 @@ - To be added. - To be added. - To be added. + A complex number. + Returns a value that indicates whether the specified complex instance is not a number (NaN). + if the specified value is not finite nor infinite; otherwise, . To be added. @@ -1570,6 +1635,32 @@ + + + Multiplies a specified number by another specified number, where at least one of them is a complex number, and the other could be a double-precision real number. + + + methods allow performing multiplication operations that involve complex numbers. + + If the multiplication results in an overflow in either the real or imaginary component, the value of that component is either or . + + The method is implemented for languages that do not support custom operators. Its behavior is identical to multiplication using the multiplication operator. + + +## Examples + The following example multiples a complex number by each element in an array of complex numbers. + + [!code-csharp[System.Numerics.Complex.Multiply#1](~/samples/snippets/csharp/VS_Snippets_CLR_System/system.numerics.complex.multiply/cs/multiply1.cs#1)] + [!code-vb[System.Numerics.Complex.Multiply#1](~/samples/snippets/visualbasic/VS_Snippets_CLR_System/system.numerics.complex.multiply/vb/multiply1.vb#1)] + + ]]> + + + @@ -1596,11 +1687,21 @@ - To be added. - To be added. - To be added. - To be added. - To be added. + The double-precision real number to multiply. + The complex number to multiply. + Returns the product of a double-precision real number and a complex number. + The product of the and parameters. + + + + @@ -1629,11 +1730,21 @@ - To be added. - To be added. - To be added. - To be added. - To be added. + The complex number to multiply. + The double-precision real number to multiply. + Returns the product of a complex number and a double-precision real number. + The product of the and parameters. + + + + @@ -1685,18 +1796,6 @@ (ac - bd) + (ad + bc)i - If the multiplication results in an overflow in either the real or imaginary component, the value of that component is either or . - - The method is implemented for languages that do not support custom operators. Its behavior is identical to multiplication using the multiplication operator. - - - -## Examples - The following example multiples a complex number by each element in an array of complex numbers. - - [!code-csharp[System.Numerics.Complex.Multiply#1](~/samples/snippets/csharp/VS_Snippets_CLR_System/system.numerics.complex.multiply/cs/multiply1.cs#1)] - [!code-vb[System.Numerics.Complex.Multiply#1](~/samples/snippets/visualbasic/VS_Snippets_CLR_System/system.numerics.complex.multiply/vb/multiply1.vb#1)] - ]]> @@ -1724,7 +1823,7 @@ System.Numerics.Complex - To be added. + Represents a complex instance that is not a number (NaN). To be added. @@ -1906,7 +2005,7 @@ Languages that do not support custom operators can call the - +