# 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:
AB
1 =IMSIN( 0.5 )
2 =IMSIN( "3+0.5i" )
32-i=IMSIN( A3 )
4 =IMSIN( COMPLEX( 1, -1 ) )
Results:
AB
1 0.479425538604203
2 0.15913058529844-0.515880442452527i
32-i1.40311925062204+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.