+0  
 
0
88
1
avatar

Four complex numbers form the vertices of a square in the complex plane. Three of the numbers are -19+32i, -5+12i and -22+15i. What is the fourth number?

 Jun 7, 2022
 #1
avatar+124676 
+1

Just set  up   as coordinates in the real plane

 

(-19, 32)  = A

(-5, 12)  = C

(-22,15)=   B 

 

Note that from B  to C, x changes by  17   and y changes   by    -3

 

So the remaining coordinate =  (-19 + 17, 32 - 3) =   (-2, 29)   =  D

 

Expressing this in complex form   =  -2 + 29i

 

See  here  :

 

 

 

cool cool cool

 Jun 7, 2022

24 Online Users