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# Precalc repost

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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
+287
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I actually figured it out, it is 48

Jan 4, 2020