Geometrical Representation of a Conjugate of a Complex Number | GeoGebra...

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.