In this article, we will learn about how to use the IMTAN function in Excel.
COMPLEX number (inumber) in excel derived for mathematical number having real and imaginary coefficients. In mathematics we call it the coefficient of i or j (iota).
i = √-1
Square root of negative number is not possible, so for calculation purpose, √-1 is named as imaginary and call it iota (i or j). For calculation of some term like shown below.
= 2 +√-25
= 2 +√-1*25
= 2 +√-1*25
= 2 +√-1* 5
= 2 + 5i
This here equation is a Complex number (inumber) having 2 different parts called real part & imaginary part
The coefficient of iota (i) which is 5 is called as imaginary part and the other part 2 is called the real part of the complex number.
Complex number (inumber) is written in the X iY format.
Complex tangent of a complex number (X + iY) is given by
Tan (X + iY) Sin (X + iY) / Cos (X + iY)
So to calculate the above equation we will use the below two equations.
Sin (X + iY) Sin (X) * Cosh (Y) + i Cos (X) * Sinh (Y)
Cos (X + iY) Cos (X) * Cosh (Y) - i Sin (X) * Sinh (Y)
Here X & Y are the coefficients of the real & imaginary part of the complex number (inumber).
The IMTAN function returns the complex tangent of the complex number (inumber) having both real & imaginary part.
inumber : complex number having both real & imaginary
Let’s understand this function using it in an example.
Here we have values where we need to get the complex Sine of the input complex number (inumber)
Use the formula:
A2 : complex number (inumber) provided as cell reference.
As you can see the complex number having real_num = 4 & imaginary part = 3. The formula returns the complex Sine of the complex number using the following formulation.
Sin (4 + 3i) Sin (4) * Cosh (3) + i Cos (4) * Sinh (3)
Cos (4 + 3i) = Cos (4) * Cosh (3) - i Sin (4) * Sinh (3)
Tan (4 + 3i) = Sin (4 + 3i) / Cos (4 + 3i)
Now copy the formula to the other remaining cells using Ctrl + D shortcut key.
As you can see the IMTAN function formula giving results just fine.
The table show here explains more about the input complex number & how excel reads it.
|inumber||Real part (X)||Imaginary part (Y)|
|i = 0 + 1i||0||1|
|1 = 1 + 0i||1||0|
Hope you understood how to use IMTAN function and referring cell in Excel. Explore more articles on Excel mathematical functions here. Please feel free to state your query or feedback for the above article.
The applications/code on this site are distributed as is and without warranties or liability. In no event shall the owner of the copyrights, or the authors of the applications/code be liable for any loss of profit, any problems or any damage resulting from the use or evaluation of the applications/code.