In the complex plane, what is the length of the diagonal of the square with vertices 4, 3+5i, -2+4i, and -1-i?

mathtoo Dec 26, 2018

#1**+1 **

The two vertices we can look at are 3 + 5i and -1 - i

Taking the difference between these complex numbers produces a complex vector =

(3 + 5i) - ( -1 - i) = 4 + 6i

The length of the diagonal is the length of this vector =

√[ 4^2 + 6^2 ] = √ [ 16 + 36 ] = √ 52 = 2√13 units

Checking that this is correct the other two vertices are 4 + 0i and - 2 + 4i

Take the difference of these two complex numbers and we get

6 - 4i

And the length of the diagonal is √ [ 6^2 + (-4)^2 ] = √52 = 2√13 units

So....true!!!

CPhill Dec 26, 2018