+817 In the complex plane, what is the length of the diagonal of the square with vertices 4, 3+5i, -2+4i, and -1-i?
+129899 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!!!
