The type **`complex128`** in Golang is the set of all complex numbers with `float64` real and imaginary parts.

Complex numbers consist of a real and an imaginary part, as illustrated below:

To create a `complex128` number in Golang, you can use the in-built `complex` function. The prototype of the `complex` function is shown below:

```Go
func complex(real, imaginary FloatType) ComplexType
```

If you provide the `complex` function with arguments of type `float64`, it returns a type `complex128` value.

An alternative method of creating a complex number is as follows:

```Go
temp := 1 + 4i 
```
The declaration shown above creates a complex number, with $1$ as the real part and $4i$ as the imaginary part.

<h2>Operations</h2>

The `complex128` type supports the usual [complex number operations](https://saylordotorg.github.io/text_intermediate-algebra/s08-07-complex-numbers-and-their-oper.html), e.g., addition, subtraction, multiplication, division, etc. 

<h2>Example</h2>

The code below shows how the `complex128` type works in Golang:

package main

import (
	"fmt"
)

func main() {

  // initializing real and imaginary parts
	var real float64 = 5
	var img float64 = 10

  // intiializing complex numbers
	complex1 := complex(real, img)  
	complex2 := 2 + 4i  
	
	// performing arithmetic operations
  fmt.Println("Addition: ", complex1, " + ", complex2, " = ", complex1 + complex2)
  fmt.Println("Subtraction: ", complex1, " - ", complex2, " = ", complex1 - complex2)
  fmt.Println("Multiplication: ", complex1, " * ", complex2, " = ", complex1 * complex2)
  fmt.Println("Division: ", complex1, " / ", complex2, " = ", complex1 / complex2)

}


<h2>Explanation</h2>

First, the code initializes two `complex128` values: `complex1` and `complex2`. `complex1` is initialized using the in-built `complex` function by providing it with two `float64` values. `complex2` is initialized using the Golang shorthand assignment operator.

Lines $18-21$ perform the arithmetic operations on the `complex128` values and output the results accordingly. These arithmetic operations follow the [mathematical rules](https://saylordotorg.github.io/text_intermediate-algebra/s08-07-complex-numbers-and-their-oper.html) defined for complex numbers.



What is type complex128 in Golang?

complex128 in Golang represents complex numbers with float64 real and imaginary parts, supporting standard complex operations.