# CV19

Show that the four points in the Argand plane represented by the complex numbers are the vertices of a square

From the given complex numbers,we can derive the points in the plane as

Let the points represent the four sides of a squate respectively

Now writing the line equation

Simplifying further we get

Now writing the line equation

Now writing the line equation

Now writing the line equation

The slope of

The slope of

The slope of

The slope of

From these slopes,the slopes of opposite sides are equal,which means they are parallel to each other and product of the one to the next is -1,which means they are perpendicular.
The lenth of

The lenth of

The lenth of

The lenth of

From the above all the sides are equal.
Hence all these conditions prove that the numbers form the vertices of a square.