If you are using a different platform, see Shortcut Keys. There will be differences for other platforms. Note for non-Windows users : The keystrokes given in this document are for Windows. Refer to Help>Quick Reference for basic Getting Started tips. Solve an Ordinary Differential Equation? Learn more about available tools and features, such as palettes and the context panel. topics cover the essentials for doing mathematics in Maple. Thereafter, clicking on ⅈ, ȷ, or I in the Common Symbols palette, or typing the letter j, will produce the imaginary unit, and its symbol as displayed in any output will be ȷ. Here, we set j to be the symbol for the imaginary unit. The calling sequence is interface(imaginaryunit=symbol) Recall that FOIL is an acronym for multiplying First, Outer, Inner, and Last terms together. To change the symbol used for the imaginary unit, (both for input and output), use the interface command. We can use either the distributive property or the FOIL method. By changing this setting, you change the output display. Furthermore, ordinarily in output the imaginary unit is displayed with a capital I, no matter which symbol was used for input. This will enable you to simply type this symbol to get − 1. You can customize the setting that specifies which symbol represents the imaginary unit. For example, x 2 + 1 = 0 → solve x = I, x = − I. Results are displayed using I for the constant − 1. įrom the Common Symbols palette: ⅈ, ȷ, and I all mean the imaginary constant. Typing I results in the imaginary constant. For instance, as the index in expressions such as seq i 2, i = 1. When you type the letter i or j in Maple, it is understood as the name `i` or `j`. Note that simply typing i will not produce the imaginary unit, but typing I will. From the palette, the symbols ⅈ, ȷ, and I can all be used to enter a complex number. You can also enter complex numbers using the Common Symbols palette. Note that the multiplication symbol is needed between the two expressions in parentheses.ġ + 2 I ⋅ 3 + 4 I = −5 + 10 I Press Ctrl + = to evaluate the expression inline. (Alternatively, use * for multiplication.) Put a space between 2 and I to signify multiplication. Multiply 1 + 2 I by 3 + 4 I and display the result inline. Using a Different Symbol for the Imaginary Unit For instance, you may want to use i or j as the imaginary unit instead of I. Maple provides a way to customize the manner in which complex numbers are displayed. The example below demonstrates two ways to enter a complex number in Maple. Thus, 1 + 2 I is a complex number in Maple. Suppose I want to divide 1 + i by 2 - i.In Maple, the default representation of the imaginary unit − 1 is I. In other words, there's nothing difficult about dividing - it's the simplifying that takes some work. Dividing Complex Numbersĭividing complex numbers is actually just a matter of writing the two complex numbers in fraction form, and then simplifying it to standard form. We'll use this concept of conjugates when it comes to dividing and simplifying complex numbers. Thus, the conjugate of 3 + 2i is 3 - 2i, and the conjugate of 5 - 7i is 5 + 7i. Every complex number has a conjugate, which we obtain by switching the sign of the imaginary part. We have a fancy name for x - yi we call it the conjugate of x + yi. It turns out that whenever we have a complex number x + yi, and we multiply it by x - yi, the imaginary parts cancel out, and the result is a real number. This is very interesting we multiplied two complex numbers, and the result was a real number! Would you like to see another example where this happens? Now we need to remember that i 2 = -1, so this becomesĬonveniently, the imaginary parts cancel out, and -16i 2 = -16(-1) = 16, so we have: Use the distributive property to write this as I say "almost" because after we multiply the complex numbers, we have a little bit of simplifying work. Multiplying complex numbers is almost as easy as multiplying two binomials together. In this section we will learn how to multiply and divide complex numbers, and in the process, we'll have to learn a technique for simplifying complex numbers we've divided.
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