# 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

## Basic Description

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

The format of the function is:

IMSIN( 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.

Therefore, the inumber argument can be supplied to the Excel Imsin function as either:

• A simple number
or
• A complex number encased in quotation marks - eg. "5+3i"
or
• A reference to a cell containing a complex number or a numeric value
or
• A value returned from another Excel function or formula

These are all included in the examples below.

## Imsin Function Examples

The spreadsheet below shows 4 different examples of the Imsin function.

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 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.

Further information and examples of the Excel Imsin function can be found 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 #NAME? - Occurs when Analysis ToolPak add-in is not enabled in your Excel.You will need to enable the add-in if you want to use the Excel complex number functions.