IMSINH Function

Basic Description

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

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

Syntax: IMSINH( inumber )

where the inumber argument is a complex number.

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

The spreadsheet below 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 cell B1 of the above spreadsheet, the supplied inumber argument is the real number 0.5, which is equal to the complex number 0.5+0i.

 

Imsinh Function Errors

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

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

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