How to use the IMSEC function
What is the IMSEC function?
The IMSEC function calculates the secant of a complex number in x + yi or x + yj text format.
The letter j is used in electrical engineering to distinguish between the imaginary value and the electric current.
What is a complex number?
What is a secant?
The trigonometric secant is a function that defines an angle of a right-angled triangle to the ratio of the hypotenuse to the adjacent side. It is also the inverse of the cosine, sec(θ) = 1/cos(θ).
What is the difference between a secant and a complex secant?
The difference between secant and secant for complex numbers is that the former is defined for real numbers, while the latter is defined for complex numbers.
The secant of a real number x is defined as sec(θ) = 2/(eθ + e-θ)
Natural number e is the base of the natural logarithm.
The secant of a complex number z = x + yi is defined as sec(x + yi) = (cos x cos y + isin x sinh y) / (cos2 x cosh2 y+ sin2 x sinh2 y)
Complex numbers has i as the imaginary unit.
Table of Contents
1. IMSEC Function Syntax
IMSEC(inumber)
2. IMSEC Function Arguments
| inumber | Required. A complex number in x+yi or x+yj text format. |
3. IMSEC function example
The image above shows a formula in cell B28 that calculates the cotangent of a complex number specified in cell B25.
Cell C28 calculates the real number from the complex number in cell B28. Cell D28 extracts the imaginary number from the complex number specified in cell B28.
The real and imaginary numbers separated in a cell each allow us to graph the complex number on the complex plane.
Formula in cell B28:
The chart above shows the complex plane, the y-axis is the imaginary axis and the x-axis is the real axis.
Complex number 2+i is the light blue line in the first quadrant. The complex secant of 2+i is the green line located in the second quadrant.
3.1 Explaining formula
Step 1 - Populate arguments
IMSEC(inumber)
becomes
IMSEC(B25)
Step 2 - Evaluate the IMSEC function
IMSEC(B25)
becomes
IMSEC("1+2i")
and returns
-0.41314934426694+0.687527438655479i
4. How is the IMSEC function calculated in detail?
The secant of a complex number is calculated like this:
C = x + yi
IMSEC(C) = (cos x cosh y + isin x sinh y) / (cos2 x cosh2 y+ sin2 x sinh2 y)
For example, C=2+i
IMSEC(2+i) = (cos 2 cosh 1 + isin 2 sinh 1) / (cos2 2 cosh2 1+ sin2 2 sinh2 1)
becomes
IMSEC(2+i) = (-0.416146836547142*1.54308063481524 + i0.909297426825682*1.1752011936438) / (0.173178189568194*2.38109784554182+ 0.826821810431806*1.38109784554182)
becomes
IMSEC(2+i) = (-0.64214812471552 + i1.06860742138278) / (0.412354214075659+ 1.14192182103435)
equals
IMSEC(2+i) = -0.41314934426694+0.687527438655479i
5. IMSEC function not working - #NUM error
The IMSEC function returns a #NUM error if the provided argument is not a valid complex number.
Useful links
IMSEC function - Microsoft
Secant of Complex Number
Complex number - Wikipedia
'IMSEC' function examples
The following article has a formula that contains the IMSEC function.
Table of Contents How to use the IMDIV function How to use the IMEXP function How to use the IMLN […]
Functions in 'Engineering' category
The IMSEC function function is one of 42 functions in the 'Engineering' category.
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