Basics of Complex Numbersdoi:10.1007/978-3-031-79176-5_1Willms, Allan R.
Week 1 Complex numbers: the basics 1. The definition of complex numbers and basic operations 2. Roots, exponential function, and logarithm 3. Multivalued functions, or dependences 1. The definition of complex numbers and basic operations ۞ The set of complex numbers can be viewed as the Euc...
The Enumerate class also supports several more complex set operations, using the Enumerable.Join, Enumerable.GroupBy, and Enumerable.GroupJoin methods. I will describe and demonstrate each of these methods in a moment. Imagine that some method hands you two sequences that are related, ...
You'll see two instances of the same window. Click to open the combobox on the left side of the window. Note that the control contains the numbers 0 through 2, corresponding to the three current customers. Choose 1, which selects Ana Trujillo and copies her name into the textbox. In ...
Note: You cannot pan or zoom vertically when Auto Zoom Heightis selected. Auto Zoom Height and Fit Auto Zoom Height Toggles Auto Zoom Height mode, which automatically scales the height of the graph so that it fits the height of the Graph Editor. The horizontal zoom must still be adjusted ...
Notice there are a few things different about this formula compared to the formula we used for the Margin calculated column. In particular, we introduced a function, SUM. Functions are pre-written formulas that make it easier to do complex calculations and manipulations with numb...
After running these two lines, the numbers variable contains the integers between 1 and 100, in random order. The behavior of this simple yet elegant solution counts on the System.Linq.Enumerable class, which provides a few dozen shared methods called extension methods that allow you to manipulat...
playing a different sound depending on whether the user makes a match or not. I decided to limit my sound support to .wav files, instead of trying to support more complex sound files such as .wma. This choice meant that I could use the PlaySound API, instead of trying to wo...
Learn about the basics of creating and working with expressions.When you want to create and link complex animations but want to avoid creating tens or hundreds of keyframes by hand, try using expressions. An expression is a small piece of JavaScript code that you can plug into animated ...
It’s worth keeping in mind that floating point numbers, such as those in float64 and float32 arrays, are only capable of approximating fractional quantities. In complex computations, you may accrue some floating point error, making comparisons only valid up to a certain number of decimal places...