GeoGebra in Mathematics

The conjugate of a complex number a + bi is a - bi . Geometrically, this represents a reflection of the original complex number across the real axis in the complex plane. To visualize this, imagine a complex plane with the real axis (x-axis) and the imaginary axis (y-axis). The complex number a + bi is represented by a point in this plane, with a as the x-coordinate and b as the y-coordinate. The conjugate, a - bi , has the same x-coordinate ( a ) but the opposite y-coordinate ( -b ). This means the point is reflected across the real axis, resulting in a mirror image of the original point. For example, if we have the complex number 3 + 4i , its conjugate is 3 - 4i . In the complex plane, 3 + 4i is represented by the point (3, 4), and its conjugate 3 - 4i is represented by the point (3, -4), which is a reflection of the original point across the real axis.

Open GeoGebra : If you haven’t already, open GeoGebra on your computer or use the online version. Create Points : Click on the “Point” tool and create three points (let’s call them A, B, and C) anywhere on the canvas. These points will be the vertices of your triangle. Connect the Points : Click on the “Segment” tool and draw segments connecting points A, B, and C. This will form your triangle. Measure Angles and Sides (Optional) : You can use the “Angle” and “Distance” tools to measure the angles and sides of your triangle. Simply click on the relevant points or segments to get the measurements. Customize Labels (Optional) : You can customize the labels of the points and segments by right-clicking on them and selecting “Object Properties.” This allows you to change their names or display values. Adjust Appearance (Optional) : You can adjust the appearance of your triangle by changing line styles, colors, and other properties using the “Style” menu. Remember that GeoGebra provides a dy...