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There are four complex numbers  such that

 

z¯z3+¯zz3=350,


and both the real and imaginary parts of z are integers. These four complex numbers are plotted in the complex plane. Find the area of the quadrilateral formed by the four complex numbers as vertices.

 Jan 1, 2020
 #1
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Let z = a + bi.  Then from the given equations, a = plus or minus 3, and b = plus or minus 5.  So, the quadrialteral is a 6 by 10 rectangle, which has an area of 60.

 Jan 3, 2020
 #2
avatar+296 
+1

I actually figured it out, it is 48

 Jan 4, 2020

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