diff --git a/xml/System.Numerics/Complex.xml b/xml/System.Numerics/Complex.xml
index dabce831640..1764baa24bb 100644
--- a/xml/System.Numerics/Complex.xml
+++ b/xml/System.Numerics/Complex.xml
@@ -1832,6 +1832,37 @@
+
+
+ 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.
+
+
+ operator allows performing addition operations that involve complex numbers. It enables code such as the following:
+
+[!code-csharp[System.Numerics.Complex.Add#3](~/samples/snippets/csharp/VS_Snippets_CLR_System/system.numerics.complex.add/cs/add3.cs#3)]
+[!code-vb[System.Numerics.Complex.Add#3](~/samples/snippets/visualbasic/VS_Snippets_CLR_System/system.numerics.complex.add/vb/add3.vb#3)]
+
+If the addition results in an overflow in either the real or imaginary component, the value of that component is either or .
+
+Languages that do not support custom operators can call the equivalent group of methods instead.
+
+The operators that receive one double are more efficient than the operators that receive two Complex numbers.
+
+## Examples
+
+The following example illustrates addition with complex numbers:
+
+[!code-csharp[System.Numerics.Complex.Add#2](~/samples/snippets/csharp/VS_Snippets_CLR_System/system.numerics.complex.add/cs/add2.cs#2)]
+[!code-vb[System.Numerics.Complex.Add#2](~/samples/snippets/visualbasic/VS_Snippets_CLR_System/system.numerics.complex.add/vb/add2.vb#2)]
+
+ ]]>
+
+
+
@@ -1858,11 +1889,24 @@
- 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.
+ The sum of and as a complex number.
+
+ equivalent method instead.
+
+ ]]>
+
+
@@ -1891,11 +1935,24 @@
- 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.
+ The sum of and as a complex number.
+
+ equivalent method instead.
+
+ ]]>
+
+
@@ -1930,40 +1987,50 @@
- The first value to add.
- The second value to add.
+ The first complex value to add.
+ The second complex value to add.
Adds two complex numbers.
The sum of and .
- method defines the addition operation for complex numbers. It enables code such as the following:
-
- [!code-csharp[System.Numerics.Complex.Add#3](~/samples/snippets/csharp/VS_Snippets_CLR_System/system.numerics.complex.add/cs/add3.cs#3)]
- [!code-vb[System.Numerics.Complex.Add#3](~/samples/snippets/visualbasic/VS_Snippets_CLR_System/system.numerics.complex.add/vb/add3.vb#3)]
-
- 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 that component is either or .
-
- Languages that do not support custom operators can call the method instead.
-
- The equivalent method for this operator is
-
-## Examples
- The following example illustrates addition with complex numbers.
-
- [!code-csharp[System.Numerics.Complex.Add#2](~/samples/snippets/csharp/VS_Snippets_CLR_System/system.numerics.complex.add/cs/add2.cs#2)]
- [!code-vb[System.Numerics.Complex.Add#2](~/samples/snippets/visualbasic/VS_Snippets_CLR_System/system.numerics.complex.add/vb/add2.vb#2)]
-
- ]]>
+ equivalent method instead.
+
+ ]]>
+
+
+ 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.
+
+
+ operator allows performing division operations that involve complex numbers. It enables code such as the following:
+
+[!code-csharp[System.Numerics.Complex.Divide#2](~/samples/snippets/csharp/VS_Snippets_CLR_System/system.numerics.complex.divide/cs/divide2.cs#2)]
+[!code-vb[System.Numerics.Complex.Divide#2](~/samples/snippets/visualbasic/VS_Snippets_CLR_System/system.numerics.complex.divide/vb/divide2.vb#2)]
+
+If the division results in an overflow in either the real or imaginary component, the value of that component is either or .
+
+Languages that do not support custom operators and operator overloading can call the equivalent group of method instead.
+
+The operators that receive one double are more efficient than the operators that receive two Complex numbers.
+
+ ]]>
+
+
+
@@ -1990,11 +2057,24 @@
- To be added.
- To be added.
- To be added.
- To be added.
- To be added.
+ The double-precision real value to be divided.
+ The complex value to divide by.
+ Divides a specified double-precision real number by a specified complex number.
+ The result of dividing by , as a complex number.
+
+ 2 + d2)) + (ad / (c2 + d2)i
+
+Languages that do not support custom operators and operator overloading can call the equivalent method instead.
+
+ ]]>
+
+
@@ -2023,11 +2103,24 @@
- To be added.
- To be added.
- To be added.
- To be added.
- To be added.
+ The complex value to be divided.
+ The double-precision real value to divide by.
+ Divides a specified complex number by a specified double-precision real number.
+ The result of dividing by , as a complex number.
+
+ 2) + (bc / c2)i
+
+Languages that do not support custom operators and operator overloading can call the equivalent method instead.
+
+ ]]>
+
+
@@ -2062,28 +2155,22 @@
- The value to be divided.
- The value to divide by.
+ The complex value to be divided.
+ The complex value to divide by.
Divides a specified complex number by another specified complex number.
The result of dividing by .
- method defines the division operation for complex numbers. It enables code such as the following:
-
- [!code-csharp[System.Numerics.Complex.Divide#2](~/samples/snippets/csharp/VS_Snippets_CLR_System/system.numerics.complex.divide/cs/divide2.cs#2)]
- [!code-vb[System.Numerics.Complex.Divide#2](~/samples/snippets/visualbasic/VS_Snippets_CLR_System/system.numerics.complex.divide/vb/divide2.vb#2)]
-
- The division of a complex number, a + bi, and a second complex number, c + di, takes the following form:
-
- ((ac + bd) / (c2 + d2)) + ((bc - ad) / (c2 + d2)i
-
- If the division results in an overflow in either the real or imaginary component, the value of that component is either or .
-
- Languages that do not support custom operators and operator overloading can call the method instead.
-
- The equivalent method for this operator is ]]>
+ 2 + d2)) + ((bc - ad) / (c2 + d2)i
+
+Languages that do not support custom operators and operator overloading can call the equivalent method instead.
+
+ ]]>
@@ -2851,6 +2938,30 @@ This API is not CLS-compliant.
+
+
+ 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.
+
+
+ operator allows performing multiplication operations that involve complex numbers. It enables code such as the following:
+
+[!code-csharp[System.Numerics.Complex.Multiply#2](~/samples/snippets/csharp/VS_Snippets_CLR_System/system.numerics.complex.multiply/cs/multiply2.cs#2)]
+[!code-vb[System.Numerics.Complex.Multiply#2](~/samples/snippets/visualbasic/VS_Snippets_CLR_System/system.numerics.complex.multiply/vb/multiply2.vb#2)]
+
+If the multiplication results in an overflow in either the real or imaginary component, the value of that component is either or .
+
+Languages that do not support custom operators can call the equivalent group of methods instead.
+
+The operators that receive one double are more efficient than the operators that receive two Complex numbers.
+
+ ]]>
+
+
+
@@ -2877,11 +2988,25 @@ This API is not CLS-compliant.
- To be added.
- To be added.
- To be added.
- To be added.
- To be added.
+ The double-precision real value to multiply.
+ The complex value to multiply.
+ Multiplies a specified double-precision real number by a specified complex number.
+ The product of and , as a complex number.
+
+ equivalent method instead.
+
+
+ ]]>
+
+
@@ -2910,11 +3035,24 @@ This API is not CLS-compliant.
- To be added.
- To be added.
- To be added.
- To be added.
- To be added.
+ The complex value to multiply.
+ The double-precision real value to multiply.
+ Multiplies the specified complex number by a specified double-precision real number.
+ The product of and , as a complex number.
+
+ equivalent method instead.
+
+ ]]>
+
+
@@ -2949,32 +3087,50 @@ This API is not CLS-compliant.
- The first value to multiply.
- The second value to multiply.
+ The first complex value to multiply.
+ The second complex value to multiply.
Multiplies two specified complex numbers.
The product of and .
- method defines the operation of the multiplication operator for complex numbers. It enables code such as the following:
-
- [!code-csharp[System.Numerics.Complex.Multiply#2](~/samples/snippets/csharp/VS_Snippets_CLR_System/system.numerics.complex.multiply/cs/multiply2.cs#2)]
- [!code-vb[System.Numerics.Complex.Multiply#2](~/samples/snippets/visualbasic/VS_Snippets_CLR_System/system.numerics.complex.multiply/vb/multiply2.vb#2)]
-
- The multiplication of a complex number, a + bi, and a second complex number, c + di, takes the following form:
-
- (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 .
-
- Languages that do not support custom operators can call the method instead.
-
- The equivalent method for this operator is ]]>
+ equivalent method instead.
+
+ ]]>
+
+
+ Subtracts a specified number from another specified number, where at least one of them is a complex number, and the other could be a double-precision real number.
+
+
+ operator allows performing subtraction operations that involve complex numbers. It enables code such as the following:
+
+[!code-csharp[System.Numerics.Complex.Subtract#2](~/samples/snippets/csharp/VS_Snippets_CLR_System/system.numerics.complex.subtract/cs/subtract2.cs#2)]
+[!code-vb[System.Numerics.Complex.Subtract#2](~/samples/snippets/visualbasic/VS_Snippets_CLR_System/system.numerics.complex.subtract/vb/subtract2.vb#2)]
+
+If the subtraction results in an overflow in either the real or imaginary component, the value of that component is either or .
+
+Languages that do not support custom operators can call the equivalent group of methods instead.
+
+The operators that receive one double are more efficient than the operators that receive two Complex numbers.
+
+ ]]>
+
+
+
@@ -3001,11 +3157,24 @@ This API is not CLS-compliant.
- To be added.
- To be added.
- To be added.
- To be added.
- To be added.
+ The double-precision real value to subtract from (the minuend).
+ The complex value to subtract (the subtrahend).
+ Subtracts a complex number from a double-precision real number.
+ The result of subtracting from , as a complex number.
+
+ method instead.
+
+ ]]>
+
+
@@ -3034,11 +3203,24 @@ This API is not CLS-compliant.
- To be added.
- To be added.
- To be added.
- To be added.
- To be added.
+ The complex value to subtract from (the minuend).
+ The double-precision real value to subtract (the subtrahend).
+ Subtracts a double-precision real number from a complex number.
+ The result of subtracting from , as a complex number.
+
+ method instead.
+
+ ]]>
+
+
@@ -3078,23 +3260,17 @@ This API is not CLS-compliant.
Subtracts a complex number from another complex number.
The result of subtracting from .
- method defines the operation of the subtraction operator for complex numbers. It enables code such as the following:
-
- [!code-csharp[System.Numerics.Complex.Subtract#2](~/samples/snippets/csharp/VS_Snippets_CLR_System/system.numerics.complex.subtract/cs/subtract2.cs#2)]
- [!code-vb[System.Numerics.Complex.Subtract#2](~/samples/snippets/visualbasic/VS_Snippets_CLR_System/system.numerics.complex.subtract/vb/subtract2.vb#2)]
-
- If the method call results in an overflow in either the real or imaginary component, the value of that component is either or .
-
- The subtraction of a complex number, c + di, from another complex number, a + bi, takes the following form:
-
- (a - c) + (b - d)i
-
- Languages that do not support custom operators can call the method instead.
-
- The equivalent method for this operator is ]]>
+ method instead.
+
+ ]]>
@@ -3572,6 +3748,34 @@ This API is not CLS-compliant.
+
+
+ Subtracts a specified number from another specified number, where at least one of them is a complex number, and the other could be a double-precision real number, and returns the result.
+
+
+ method allows subtraction operations that involve complex numbers.
+
+If the subtraction results in an overflow in either the real or imaginary component, the value of that component is either or .
+
+Languages that support custom operators can use the equivalent group of operators too.
+
+The methods that receive one double are more efficient than the method that receive two Complex numbers.
+
+## Examples
+
+The following example subtracts each complex number in an array from a complex number:
+
+[!code-csharp[System.Numerics.Complex.Subtract#1](~/samples/snippets/csharp/VS_Snippets_CLR_System/system.numerics.complex.subtract/cs/subtract1.cs#1)]
+[!code-vb[System.Numerics.Complex.Subtract#1](~/samples/snippets/visualbasic/VS_Snippets_CLR_System/system.numerics.complex.subtract/vb/subtract1.vb#1)]
+
+ ]]>
+
+
+
@@ -3598,11 +3802,24 @@ This API is not CLS-compliant.
- To be added.
- To be added.
- To be added.
- To be added.
- To be added.
+ The double-precision real value to subtract from (the minuend).
+ The complex value to subtract (the subtrahend).
+ Subtracts one complex number from a double-precision real number and returns the result.
+ The result of subtracting from , as a complex number.
+
+ equivalent operator too.
+
+ ]]>
+
+
@@ -3631,11 +3848,24 @@ This API is not CLS-compliant.
- To be added.
- To be added.
- To be added.
- To be added.
- To be added.
+ The complex value to subtract from (the minuend).
+ The double-precision real value to subtract (the subtrahend).
+ Subtracts one double-precision real number from a complex number and returns the result.
+ The result of subtracting from , as a complex number.
+
+ equivalent operator too.
+
+ ]]>
+
+
@@ -3680,26 +3910,17 @@ This API is not CLS-compliant.
Subtracts one complex number from another and returns the result.
The result of subtracting from .
- or .
-
- Languages that do not support custom operators can use the method to perform subtraction using complex numbers.
-
-
-
-## Examples
- The following example subtracts each complex number in an array from a complex number.
-
- [!code-csharp[System.Numerics.Complex.Subtract#1](~/samples/snippets/csharp/VS_Snippets_CLR_System/system.numerics.complex.subtract/cs/subtract1.cs#1)]
- [!code-vb[System.Numerics.Complex.Subtract#1](~/samples/snippets/visualbasic/VS_Snippets_CLR_System/system.numerics.complex.subtract/vb/subtract1.vb#1)]
-
- ]]>
+ equivalent operator too.
+
+ ]]>
@@ -4123,4 +4344,4 @@ This API is not CLS-compliant.
-
\ No newline at end of file
+