IMSINH

Returns the hyperbolic sine of a complex number.

Syntax

IMSINH( z )

where z is a complex

Semantics

IMSINH("a+bj") calculates

$s inh (a) cos (b) + cos h (a) s in (b) j$

Application:

Transmission Line Analysis

Imagine we have a transmission line with a characteristic impedance Z0 and propagation constant γ. Both of these are complex numbers. To find the voltage and current at a specific point on the line, we might need to use hyperbolic functions of complex numbers. The IMSINH function helps us calculate this.

Let's assume the propagation constant is represented as a complex number inumber. We can use the IMSINH function to find the hyperbolic sine of this value.

Here's a table illustrating how the IMSINH function would be used with different complex numbers representing the propagation constant of a transmission line:

	Complex Number (Propagation Constant)	Formula	Result of IMSINH
	A	B	C
1	1+2i	IMSINH("1+2i")	1.40312 + 2.30129i
2	3+4i	IMSINH("3+4i")	10.01788 + 9.15470i
3	5+6i	IMSINH("5+6i")	74.20321 + 51.12514i
4	0.5+0.8i	IMSINH("0.5+0.8i")	0.58474 + 0.90097i

In this table, the first column contains the complex numbers representing the propagation constant. The second column shows the IMSINH function being applied to these numbers (as text strings, which is a common way to input them into spreadsheet software). The third column shows the complex number output, which is the hyperbolic sine of the input. This output value would then be used in further calculations to determine the voltage, current, and other critical parameters of the transmission line.