The Excel IMCOS Function
Related Function:IMSIN Function
Cosine of a Complex Number
The cosine of a complex number is calculated by the following equation:
cos(x + yi) = cos(x) cosh(y) - sin(x) sinh(y)i
for more information on complex numbers.
The Excel Imcos function returns the cosine of a supplied complex number.
The syntax of the function is:
IMCOS( inumber )
where the inumber argument is the complex number that you want to calculate the cosine 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.
Imcos Function Examples
In the spreadsheets below, the Excel Imcos function is used to calculate the cosine of 4 different complex numbers.
|1|| ||=IMCOS( 0.5 )|
|2|| ||=IMCOS( "3+0.5i" )|
|3||2-i||=IMCOS( A3 )|
|4|| ||=IMCOS( COMPLEX( 1, -1 ) )|
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 Imcos function are provided on the Microsoft Office website
Imcos Function Errors
If you get an error from the Excel Imcos Function, this is likely to be one of the following:
|#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.|