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IMSIN Function

Excel 2007+

Summary

The Excel IMSIN function calculates the sine of a complex number provided in x+yi or x+yj format. This engineering function is essential for advanced mathematical computations involving complex numbers.

Syntax

IMSIN(inumber)

Parameters

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

Using the IMSIN Function

IMSIN is used in engineering, physics, and electrical calculations where complex numbers are involved. Convert real and imaginary parts to complex format using the COMPLEX function before applying IMSIN.

Common IMSIN Examples

Basic IMSIN Example

=IMSIN("4+3i")

Calculates sine of complex number 4+3i, returning approximately -7.619-6.548i

With COMPLEX Function

=IMSIN(COMPLEX(4,3))

Creates complex number from real(4) and imaginary(3) parts, then calculates sine

Frequently Asked Questions

Use x+yi or x+yj text format, like "4+3i" or "4+3j".

Use the COMPLEX(real_num, i_num) function to convert separate real and imaginary parts.

Available in Excel 2007 and later versions.

Common Errors and Solutions

#VALUE! error

Cause: inumber is not a valid complex number

Solution: Ensure inumber follows x+yi or x+yj format, or use COMPLEX() function

#NUM! error

Cause: Invalid complex number format

Solution: Check that real and imaginary coefficients are valid numbers

Notes

The mathematical formula for sine of complex z is sin(z) = (e^(iz) - e^(-iz))/(2i)
Use COMPLEX to create complex numbers from real/imaginary coefficients
IMSIN returns results in x+yi format
Part of Excel's 60+ complex number functions

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+