The Excel IMSIN Function

Related Function:

IMCOS Function

Sine of a Complex Number

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

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

See Wikipedia for more information on complex numbers.

Function Description

The Excel Imsin function returns the Sine of a supplied complex number.

The syntax of the function is:

IMSIN( inumber )

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

Imsin Function Examples

In the spreadsheets below, the Excel Imsin function is used to calculate the sine of 4 different complex numbers.

Formulas:

	A	B
1		=IMSIN( 0.5 )
2		=IMSIN( "3+0.5i" )
3	2-i	=IMSIN( A3 )
4		=IMSIN( COMPLEX( 1, -1 ) )

Results:

	A	B
1		0.479425538604203
2		0.15913058529844-0.515880442452527i
3	2-i	1.40311925062204+0.489056259041294i
4		1.29845758141598-0.634963914784736i

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 and examples of the Excel Imsin function are provided on the Microsoft Office website

Imsin Function Errors

If you get an error from the Excel Imsin 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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