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

See Wikipedia for more information on complex numbers.

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.

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