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IMSINH Function

Excel 2013+

Summary

The IMSINH function computes the hyperbolic sine of a complex number provided in x+yi or x+yj format. This advanced mathematical function is essential for engineering calculations and scientific analysis involving complex numbers.

Syntax

IMSINH(inumber)

Parameters

Parameter	Type	Required	Description
inumber	`Complex`	Yes	A complex number entered as text in x+yi or x+yj format

Using the IMSINH Function

IMSINH is used in advanced mathematical modeling where hyperbolic functions of complex numbers are required. Combine it with COMPLEX function to create complex numbers from real and imaginary parts.

Common IMSINH Examples

Basic IMSINH Calculation

=IMSINH("4+3i")

Calculates hyperbolic sine of 4+3i, returning approximately -27.0168+3.8537i

Using with COMPLEX function

=IMSINH(COMPLEX(4,3))

Converts real (4) and imaginary (3) parts to complex number first, then calculates hyperbolic sine

Frequently Asked Questions

Use x+yi or x+yj text format (e.g., "4+3i" or "4+3j").

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

Common Errors and Solutions

#NUM!

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

Solution: Ensure complex number uses correct format with + or - between real/imaginary parts

#VALUE!

Cause: inumber is a logical value

Solution: Provide numeric complex number in text format

Notes

Use COMPLEX(real_num, i_num) to create complex numbers from separate real and imaginary components
Result is returned in x+yi format
Part of Excel's engineering function category

Compatibility

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

Not available in: Excel 2010, Excel 2007, Excel 2003 and earlier

Content last reviewed: December 9, 2025
Update frequency: As needed
Excel versions tested: Excel 2013+