# Finding the Decimal Logarithm of Complex Number in Golang

In mathematics, a complex number is a number that comprises a real and imaginary part. A decimal logarithm is a logarithmic function with base 10. In Golang, we can use the "math/cmplx" package to find the decimal logarithm of a complex number.

## Syntax

The syntax for finding the decimal logarithm of a complex number in Golang is −

func Log10(z complex128) complex128


Here, "z" is the complex number for which we want to find the decimal logarithm.

## Example 1

Let's say we have a complex number (5+12i), and we want to find its decimal logarithm. We can do this using the following code −

package main

import (
"fmt"
"math/cmplx"
)

func main() {
z := complex(5, 12)
log := cmplx.Log10(z)
fmt.Printf("log10(%v) = %v\n", z, log)
}


## Output

log10((5+12i)) = (1.1139433523068367+0.5107325721309081i)


We first create a complex number z with the value (5+12i). We then use the Log10() function from the cmplx package to find its decimal logarithm. Finally, we print the result using fmt.Printf().

## Example 2

Let's say we have a complex number (-2+4i), and we want to find its decimal logarithm. We can do this using the following code −

package main

import (
"fmt"
"math/cmplx"
)

func main() {
z := complex(-2, 4)
log := cmplx.Log10(z)
fmt.Printf("log10(%v) = %v\n", z, log)
}


## Output

log10((-2+4i)) = (0.6505149978319906+0.8835477750576072i)

We first create a complex number z with the value (-2+4i). We then use the Log10() function from the cmplx package to find its decimal logarithm. Finally, we print the result using fmt.Printf().

## Example 3

Let's say we have a complex number (0+1i), and we want to find its decimal logarithm. We can do this using the following code −

package main

import (
"fmt"
"math/cmplx"
)

func main() {
z := complex(0, 1)
log := cmplx.Log10(z)
fmt.Printf("log10(%v) = %v\n", z, log)
}


## Output

log10((0+1i)) = (0+0.6821881769209206i)

We first create a complex number z with the value (0+1i). We then use the Log10() function from the cmplx package to find its decimal logarithm. Finally, we print the result using fmt.Printf().

## Conclusion

In this article, we have learned how to find the decimal logarithm of a complex number in Golang using the "math/cmplx" package. We have seen three examples of how to use this function to find the decimal logarithm of different complex numbers. The Log10() function takes a complex number as input and returns a complex number as output.

Updated on: 12-Apr-2023

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