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Finding the Inverse Hyperbolic Cosine of Complex Number in Golang
Golang has a built-in math package that provides various mathematical functions. In this article, we will focus on finding the inverse hyperbolic cosine of a complex number using the math/cmplx package in Golang.
Inverse Hyperbolic Cosine Function
The inverse hyperbolic cosine function (acosh) is the inverse function of the hyperbolic cosine function (cosh). It is defined for real numbers x ≥ 1, and its range is the set of non-negative real numbers. For complex numbers, acosh is defined as −
acosh(z) = ln(z + sqrt(z^2 - 1))
where ln is the natural logarithm, sqrt is the square root, and z is a complex number.
In Golang, the math/cmplx package provides the Acosh() function to find the inverse hyperbolic cosine of a complex number. The syntax of the Acosh() function is −
func Acosh(x complex128) complex128
The Acosh() function takes a complex number x as an argument and returns the inverse hyperbolic cosine of x.
Example 1: Finding the Inverse Hyperbolic Cosine of a Complex Number
Let's find the inverse hyperbolic cosine of a complex number using the Acosh() function.
package main
import (
"fmt"
"math/cmplx"
)
func main() {
// Declare a complex number
z := complex(3, 4)
// Find the inverse hyperbolic cosine of z
acosh := cmplx.Acosh(z)
// Display the result
fmt.Printf("acosh(%v) = %v\n", z, acosh)
}
Output
acosh((3+4i)) = (2.3055090312434685+0.9368124611557194i)
In this example, we first declare a complex number z using the complex() function. We then find the inverse hyperbolic cosine of z using the Acosh() function and store the result in the acosh variable. Finally, we display the result using the Printf() function.
Example 2: Finding the Inverse Hyperbolic Cosine of a Real Number
Let's find the inverse hyperbolic cosine of a real number using the Acosh() function
package main
import (
"fmt"
"math/cmplx"
)
func main() {
// Declare a real number
x := 2.5
// Find the inverse hyperbolic cosine of x
acosh := cmplx.Acosh(complex(x, 0))
// Display the result
fmt.Printf("acosh(%v) = %v\n", x, acosh)
}
Output
acosh(2.5) = (1.5667992369724106+0i)
In this example, we first declare a real number x. We then convert the real number to a complex number using the complex() function and find the inverse hyperbolic cosine of x using the Acosh() function. Finally, we display the result using the Printf() function.
Conclusion
In this article, we learned how to find the inverse hyperbolic cosine of a complex number using the Acosh() function provided by the math/cmplx package in Golang. We also saw how to find the inverse hyperbolic cosine of a real number by converting it to a complex number. The Acosh() function is a useful tool for solving mathematical problems involving complex numbers.
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