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There are four complex numbers  such that

 

\(z \overline{z}^3 + \overline{z} z^3 = 350,\)


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
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I actually figured it out, it is 48

 Jan 4, 2020

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