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IMCOS Function

Excel 2007+

Summary

The Excel IMCOS function calculates the cosine of a complex number, essential for advanced mathematical and engineering calculations involving complex arguments. It returns results in standard complex number format (x+yi).

Syntax

IMCOS(inumber)

Parameters

Parameter	Type	Required	Description
inumber	`Complex Number`	Yes	The complex number (in x+yi or x+yj text format) for which you want to find the cosine

Using the IMCOS Function

IMCOS is used in scientific, engineering, and mathematical applications where trigonometric functions must handle complex numbers. Combine with COMPLEX function to create complex arguments from real/imaginary components.

Common IMCOS Examples

Basic Complex Cosine

=IMCOS("1+i")

Calculates cosine of complex number 1+i, returning 0.833730025131149-0.988897705762865i

Using COMPLEX Function

=IMCOS(COMPLEX(2,3))

Cosine of complex number created from real part 2 and imaginary part 3

Frequently Asked Questions

Use x+yi or x+yj text format. Use COMPLEX(real_num, i_num) to create complex numbers.

IMCOS returns #VALUE! error if inumber is a logical value.

Common Errors and Solutions

#VALUE!

Cause: inumber is logical value or invalid complex format

Solution: Ensure proper complex number format using COMPLEX function

#NUM!

Cause: Invalid complex number format

Solution: Use quotes for text format: "3+4i" or COMPLEX(3,4)

Notes

Formula: cos(z) = (e^(iz) + e^(-iz))/2 where z is complex
Use COMPLEX to convert real/imaginary coefficients
Pair with IMSIN, IMCOSH for complete complex trig functions
Result precision matches Excel's complex calculation engine

Compatibility

Available in: Excel 2007, Excel 2010, Excel 2013, Excel 2016, Excel 2019, Excel 2021, Microsoft 365

Not available in: Excel 2003 and earlier

Content last reviewed: December 9, 2025
Update frequency: As needed
Excel versions tested: Excel 2007+