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

See Wikipedia for more information on complex numbers.

Function Description

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.

Formulas:

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

Results:

	A	B
1		0.877582561890373
2		-1.11634124452615-0.0735369737112366i
3	2-i	-0.64214812471552+1.06860742138278i
4		0.833730025131149+0.988897705762865i

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:

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.

Return to the Excel Engineering Functions Page
Return to the List of All Built-In Excel Functions