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

 Dec 26, 2018
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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!!!

 

 

cool cool cool

 Dec 26, 2018
edited by CPhill  Dec 26, 2018

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