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`