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IMCOSH Function

Excel 2007+

Summary

The Excel IMCOSH function calculates the hyperbolic cosine of a complex number entered in x+yi or x+yj format. This engineering function handles complex mathematical computations that standard COSH cannot process.

Syntax

IMCOSH(inumber)

Parameters

Parameter	Type	Required	Description
inumber	`Complex Number`	Yes	The complex number for which to calculate the hyperbolic cosine. Must be in x+yi or x+yj format.

Using the IMCOSH Function

IMCOSH is vital for advanced engineering calculations involving complex numbers, particularly in electrical engineering, signal processing, and control systems where hyperbolic functions of complex arguments appear.

Common IMCOSH Examples

Basic Complex Hyperbolic Cosine

=IMCOSH("4+3i")

Calculates hyperbolic cosine of 4+3i, returning -27.0349456030742+3.85115333481178i

Using COMPLEX Helper Function

=IMCOSH(COMPLEX(4,3))

Converts real/imaginary parts to complex number first, then calculates hyperbolic cosine.

Frequently Asked Questions

Must be text in x+yi or x+yj format. Use COMPLEX() function to create from real/imaginary parts.

Returns #NUM! error if not in proper x+yi or x+yj text format.

Common Errors and Solutions

#NUM!

Cause: inumber not in valid x+yi or x+yj format

Solution: Ensure proper complex number format or use COMPLEX(real_num, i_num)

#VALUE!

Cause: inumber is logical value

Solution: Provide numeric complex number in correct format

Notes

Use COMPLEX(real_number, imaginary_number) to create complex numbers programmatically
Both 'i' and 'j' imaginary unit notations supported
Result always returned as complex number in x+yi format

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+