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avatar+29 

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

 

Also: I don't really get how to do this problem visually, because these points don't have a y coordinate

 May 14, 2019
 #1
avatar+102417 
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We can just label the points  as  (4, 0) (3,5) (-2, 4) and (-1, -1)

 

The distance between (3, 5)  and   (-1, -1)  will be one diagonal   

 

So....the distance is

 

sqrt [ (-1-3)^2 + ( (-1-5)^2 ] = sqrt ( (-4)^2 + (-6)^2 ]  = sqrt [ 16 + 36 ]=  sqrt [52 ]  =

 

sqrt(4) * sqrt(13)  =     2sqrt (13)  units

 

 

cool cool cool

 May 14, 2019

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