Author: Oscar CronquistArticle last updated on June 02, 2023
What is the IMSIN function?
The IMSIN function calculates the sine 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 the sine?
The sine is a trigonometric function that relates an angle θ in a right triangle to the ratio of the length of the side opposite the angle and the length of the longest side (hypotenuse) of the triangle. A right triangle has one angle that measures 90° or π/2 radians which is approximately 1.5707963267949 radians.
What is the difference between sine and the complex sine?
The difference between sine and complex sine is that the former is defined for real numbers only, while the latter is defined for complex numbers as well. The sine of a complex number has some similarities to the sine of a real number, such as periodicity.
The sine function is periodic considering the angle, meaning it repeats its values after a certain interval. The period of the sine function is 2Ï€ or 360 degrees.
The image above demonstrates a formula in cell B28 that calculates the sine 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:
=IMSIN(B25)
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+2i is the light blue line in the first quadrant. The sine of 2+2i is the green line shown in the fourth quadrant.
4. How to calculate the sine of a complex number in detail?
The sine of a complex number is calculated like this:
C = x + yi
sin (C) = sin (x) cosh (y) + cos (x) sinh (y)i
For example, C=2+2i
sin (2+2i) = sin (2) cosh (2) + cos (2) sinh (2)i
becomes
sin (2+2i) = 0.909297426825682*3.76219569108363 + -0.416146836547142*3.62686040784702i
equals
sin (2+2i) = 3.42095486111701 - 1.50930648532361i
sin - calculates the sine of a number
cos - calculates the cosine of a number
cosh - calculates the hyperbolic cosine of a number
sinh - calculates the hyperbolic sine of a number
5. IMSIN function not working
The IMSIN function returns a #NUM error if the provided argument is not a valid complex number.
Functions for backward compatibility with earlier Excel versions. Compatibility functions are replaced with newer functions with improved accuracy. Use the new functions if compatibility isn't required.
These functions let you sort, lookup, get external data like stock quotes, filter values based a condition or criteria, and get the relative position of a given value in a specific cell range. They also let you calculate row, column, and other properties of cell references.
Functions that let you manipulate text values, substitute strings, find string in value, extract a substring in a string, convert characters to ANSI code among other functions.
More than 300 Excel functions with detailed information including syntax, arguments, return values, and examples for most of the functions used in Excel formulas.
Excel Tables simplifies your work with data, adding or removing data, filtering, totals, sorting, enhance readability using cell formatting, cell references, formulas, and more.
Allows you to filter data based on selected value , a given text, or other criteria. It also lets you filter existing data or move filtered values to a new location.
Lets the user work more efficiently by showing a list that the user can select a value from. This lets you control what is shown in the list and is faster than typing into a cell.
Lets you name one or more cells, this makes it easier to find cells using the Name box, read and understand formulas containing names instead of cell references.
The Excel Solver is a free add-in that uses objective cells, constraints based on formulas on a worksheet to perform what-if analysis and other decision problems like permutations and combinations.
Format cells or cell values based a condition or criteria, there a multiple built-in Conditional Formatting tools you can use or use a custom-made conditional formatting formula.
Lets you quickly summarize vast amounts of data in a very user-friendly way. This powerful Excel feature lets you then analyze, organize and categorize important data efficiently.
VBA stands for Visual Basic for Applications and is a computer programming language developed by Microsoft, it allows you to automate time-consuming tasks and create custom functions.
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