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#Engineering

IMSINH

Excel Functions

Get hyperbolic sine of the complex number.

Syntax

EXCEL 
=IMSINH(complex_num)

Arguments

Parameter Description
complex_num The complex number in the form "x+yi".

Return Value

The hyperbolic sine of the complex number.

Details

The Excel IMSINH function returns the hyperbolic sine of a complex number. For example, given 1+π/2i as input, the function returns -4.10319E-15 + 1.543080635i as output. When the function's output is plotted over the complex plane, the real output along the real axis traces the shape of the SINH function. The imaginary output along the imaginary axis traces the shape of the SIN function. The function can be defined for complex input using the SIN, COS, SINH, and COSH functions, which take real numbers as input.

Examples

Example 1

The Excel IMSINH function returns the hyperbolic sine of a complex number. For example, given 1+π/2i as input, the function returns -4.10319E-15 + 1.5

EXCEL 
=IMSINH(COMPLEX(1, PI()/2)) // returns -4.10319E-15 + 1.543080635i
Example 2

When the function's output is plotted over the complex plane, the real output along the real axis traces the shape of the SINH function.

EXCEL 
=IMSINH(COMPLEX(x,0)) // returns SINH(x) + 0i
Example 3

The imaginary output along the imaginary axis traces the shape of the SIN function.

EXCEL 
=IMSINH(COMPLEX(0,y)) // returns 0 + SIN(y)i

See Also

COMPLEX SINH SIN