Finding the Inverse Tangent of Complex Number in Golang

Trigonometric functions are widely used in mathematics, physics, engineering, and many other fields. Inverse trigonometric functions are the inverse of the trigonometric functions, and they are used to find the angle when the ratio of two sides of a right-angled triangle is known. In this article, we will discuss how to find the inverse tangent of a complex number in Golang.

Finding the Inverse Tangent of a Complex Number

To find the inverse tangent of a complex number in Golang, we can use the Atan() function from the math/cmplx package. The Atan() function takes a complex number as an argument and returns the inverse tangent of the complex number.

Syntax

The syntax of the Atan() function is as follows −

func Atan(x complex128) complex128

Here, x is a complex number for which we want to find the inverse tangent.

Example 1: Finding the Inverse Tangent of a Complex Number

Let's find the inverse tangent of a complex number using the Atan() function.

package main

import (
   "fmt"
   "math/cmplx"
)

func main() {
   // Creating a complex number
   z := complex(3, 4)
   
   // Finding the inverse tangent of the complex number
   atan := cmplx.Atan(z)
   
   // Displaying the result
   fmt.Println("Inverse Tangent of", z, "is", atan)
}

Output

Inverse Tangent of (3+4i) is (1.4483069952314644+0.15899719167999918i)

Example 2: Finding the Inverse Tangent of a Negative Complex Number

Let's find the inverse tangent of a negative complex number using the Atan() function.

package main

import (
   "fmt"
   "math/cmplx"
)

func main() {
   // Creating a complex number
   z := complex(-3, -4)
   
   // Finding the inverse tangent of the complex number
   atan := cmplx.Atan(z)
   
   // Displaying the result
   fmt.Println("Inverse Tangent of", z, "is", atan)
}

Output

Inverse Tangent of (-3-4i) is (-1.4483069952314644-0.15899719167999918i)

Example 3: Finding the Inverse Tangent of a Purely Imaginary Number

Let's find the inverse tangent of a purely imaginary number using the Atan() function.

package main

import (
   "fmt"
   "math/cmplx"
)
   
func main() {
   // Creating a complex number
   z := complex(0, 5)
   
   // Finding the inverse tangent of the complex number
   atan := cmplx.Atan(z)
   
   // Displaying the result
   fmt.Println("Inverse Tangent of", z, "is", atan)
}

Output

Inverse Tangent of (0+5i) is (-1.5707963267948968+0.2027325540540822i)

Example 4: Finding the Inverse Tangent of an Imaginary Number

Let's find the inverse tangent of an imaginary number using the Atan() function.

package main

import (
   "fmt"
   "math/cmplx"
)
   
func main() {
   // Creating a complex number
   z := complex(-2, -1)
   
   // Finding the inverse tangent of the complex number
   atan := cmplx.Atan(z)
   
   // Displaying the result
   fmt.Println("Inverse Tangent of", z, "is", atan)
}

Output

Inverse Tangent of (-2-1i) is (-1.1780972450961724-0.17328679513998632i)

Conclusion

The inverse trigonometric functions are useful in solving complex mathematical problems, and Golang provides several built-in functions for finding the inverse sine, inverse cosine, inverse tangent, and inverse hyperbolic functions of complex numbers. These functions are part of the math/cmplx package and can be easily used in Golang programs.

When working with complex numbers, it is important to keep in mind that the results of these functions may also be complex numbers, and not always real numbers. Therefore, it is important to handle the output of these functions accordingly.

Overall, the ability to find the inverse trigonometric functions of complex numbers in Golang makes it a powerful tool for mathematicians, engineers, and scientists who work with complex numbers.