# The Excel IMSINH Function

Related Functions:
IMSIN Function
IMCOSH Function
Hyperbolic Sine of a Complex Number

The hyperbolic sine of a complex number is calculated by the following equation:

sinh(x + yi) = sinh(x) cos(y) - cosh(x) sin(y)i

## Function Description

The Excel Imsinh function returns the hyperbolic sine of a supplied complex number.

Note: the Imsinh function was only introduced in Excel 2013, so is not available in earlier versions of Excel.

The syntax of the function is:

IMSINH( inumber )

where the inumber argument is the complex number that you want to calculate the hyperbolic sine of.

### Complex Numbers in Excel

Note that complex numbers are simply stored as text in Excel. When a text string in the format "a+bi" or "a+bj" is supplied to one of Excel's built-in complex number functions, this is interpreted as a complex number.

Also the complex number functions can accept a simple numeric value, as this is equivalent to a complex number whose imaginary coefficient is equal to 0.

## Imsinh Function Examples

Column B of the following spreadsheet shows 4 different examples of the Imsinh function. Each example uses a different method to supply the complex number to the function.

Formulas:
A B
1   =IMSINH( 0.5 )
2   =IMSINH( "3+0.5i" )
3 2-i =IMSINH( A3 )
4   =IMSINH( COMPLEX( 1, -1 ) )
Results:
A B
1   0.521095305493747
2   8.79151234349371 + 4.82669427481082i
3 2-i 1.95960104142161 - 3.16577851321617i
4   0.634963914784736 - 1.29845758141598i

Note that, in the above example spreadsheet:

• The real number 0.5, used in cell B1, is equal to the complex number 0.5+0i;
• The example in cell B4 uses the Excel Complex Function to create the complex number 1-i.

Further details of the Excel Imsinh function are provided on the Microsoft Office website

## Imsinh Function Errors

If you get an error from the Excel Imsinh Function, this is likely to be one of the following:

Common Errors
 #NUM! - Occurs if the supplied inumber argument is not recognised as a complex number. #VALUE! - Occurs if the supplied inumber argument is a logical value.