Question

The complex numbers corresponding to the endpoints of one diagonal of a square drawn on a complex plane are 1 + 2i and -2 – i.What are the complex numbers corresponding to the endpoints of the square's other diagonal?

Answer 1

On the complex plane, the number $a+bi$ is mapped onto the point with coordinates $(a,b)$.

In other words, the x coordinate is the real part of the number, while the y coordinate is the complex part of the number.

Viceversa, if you start from a point $(x,y)$, you can identify the number $x + iy$.

So, the endpoints of the diagonal are the points $(1,2)$ and $(-2,-1)$. These are points A and C in the attached figure.

This means that points B and D have coordinates

$B = (-2,2),\quad D = (1,-1)$

So, the correspondant complex numbers are

$B = (-2,2)\mapsto -2+2i,\quad D = (1,-1)\mapsto 1-i$