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The Excel IMSIN Function
Related Function:
IMCOS FunctionSine 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.
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 builtin 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:
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:  A  B 

1   =IMSIN( 0.5 ) 

2   =IMSIN( "3+0.5i" ) 

3  2i  =IMSIN( A3 ) 

4   =IMSIN( COMPLEX( 1, 1 ) ) 

 Results:  A  B 

1   0.479425538604203 

2   0.159130585298440.515880442452527i 

3  2i  1.40311925062204+0.489056259041294i 

4   1.298457581415980.634963914784736i 


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 addin is not enabled in your Excel. You will need to enable the addin if you want to use the Excel complex number functions.
+ Show How to Do This in Excel 2003:
 From the Tools dropdown menu, select the option AddIns ...
 An 'AddIns' window will pop up. From this, select the option Analysis ToolPak and click OK
+ Show How to Do This in Excel 2007:
 Click the Microsoft button on the top left of your spreadsheet and select
the Excel Options button
 From the menu on the left hand side, select AddIns
 In the 'Manage:' box, select Excel Addins and click Go...
 An 'AddIns' window will pop up. From this, select the option Analysis ToolPak and click OK
+ Show How to Do This in Excel 2010 or Excel 2013:
 Click the File tab (top left of your spreadsheet) and select Options
 From the menu on the left hand side, select AddIns
 If the window that pops up doesn't show the 'Addins' list, use the 'Manage:'
dropdown menu (at the bottom of the window) to select Excel Addins. Click Go...
 From the 'AddIns' window, select the option Analysis ToolPak and click OK
