Complex numbers
Task
Determine a complex number and change the coordinates of the complex number to polar coordinates.
Explore the construction and learn how to visualize complex numbers on a polar coordinate grid with GeoGebra Graphing Calculator. Then try it yourself by following the instructions below.
Explore the construction...
Instructions
| 1. |  | In the Algebra View open the Input Help and choose Text. |
| 2. | | Copy the following text into the Input Bar and press Enter: |
| | | CCSS.MATH.CONTENT.HSN.CNB.4 Represent complex numbers on the complex plane in rectangular and polar form (including real and imaginary numbers), and explain why the rectangular and polar form of a given complex number represent the same number. |
| 3. |  | Open the Tools View and search for the Complex Number tool. Select this tool and click anywhere inside the Graphics View to create a complex number. Note: The complex number will automatically be labeled z1 and its coordinates will be displayed in the Algebra View. |
| 4. |  | Open the global settings and change the font size. |
| 5. |   | Select the complex number in the Graphics View and change its settings. In the label menu mark Show Value. Change the point size as well. Note: In the Mobile App open the context menu by pressing the More button. Then on Set caption style select Value. |
| 6. |  | Enter into the Input Bar, press Enter and hide the new complex number by selecting the enabled Visibility button on the left. |
| 7. |  | In the Algebra View open the context menu by pressing the More button of z2 and select Settings. Open the tab Algebra. Change the coordinates into Polar Coordinates and close the settings. The complex number z2 will now be displayed in polar coordinates in the Algebra View. Note: In the Mobile App enter in order to show its polar coordinates in the Algebra View. |
| 8. |  | Move the point z1 in the Graphics View and explore how the values change in the Algebra View. |
| 9. | | Open the Settings and select Show Grid. Activate a Polar grid. Note: In the Mobile App select Show Grid and change Grid Type to Polar. |