What is Grapher on a Mac?
Grapher is a computer program bundled with macOS since version 10.4 that is able to create 2D and 3D graphs from simple and complex equations. It includes a variety of samples ranging from differential equations to 3D-rendered Toroids and Lorenz attractors.
Graphing Complex Numbers - YouTube
To get the real or imaginary part of a number/point a, do a.x or a.y respectively. Desmos can add and subtract points just like complex numbers. To define your own complex number, type a = (real,imaginary). The points will appear in the graph like it is in the complex plane.
for example: z = 4 + 5i, where x and y are real numbers, and i is the imaginary unit. In this customary notation the complex number z corresponds to the point (x, y) in the Cartesian plane.
- Click anywhere on the graph to select it.
- Click the Home| Add to Graph | Plot command ( ).
- In the Select Plot Type dialog, click your desired plot type and then click OK. ...
- In the Choose Axes dialog, be sure to select X Axis 1 and Y Axis 1 and click OK.
- Select the data file and click Open.
How to Animate with the Graph Editor - YouTube
What Are Imaginary Numbers? The imaginary number i is equal to the square root of -1. In other words, i2 equals -1. The square root of a negative number is not a real number and it is not a variable.
The standard form of writing a complex number is z = a + ib. The standard form of the complex number has two parts, the real part, and the imaginary part. In the complex number z = a + ib, a is the real part and ib is the imaginary part.
...
| Imaginary Numbers | |
|---|---|
| 3i (b = 3) | −672i (b = −672) |
| (b = ) | (b = ) |
You find the complex conjugate simply by changing the sign of the imaginary part of the complex number. Example. To find the complex conjugate of 4+7i we change the sign of the imaginary part. Thus the complex conjugate of 4+7i is 4 - 7i.
Can you take the square root of I?
sqrt(i) - YouTube
When you need a subscript just push the alt button in the keypad. Then click on the button with the a^b power. It will switch the button to a (subscript) b. When you are finished just "left click" the mouse right next to it and begin typing the rest of the equation.
Generally a complex number is of form x+iy so real part of it is x and imaginary part is y. So, maybe z (as x and y are already used and z comes after y) is used to represent the complex number.
The vertical number line (the y-axis on a Cartesian plane) is the imaginary axis.
This negative square root creates an imaginary number. The graph of this quadratic function shows that there are no real roots (zeros) because the graph does not cross the x-axis. Such a graph tells us that the roots of the equation are complex numbers, and will appear in the form a + bi.