Let S = \z C : 4z2 + z = 0\. Then z S |z|2 is equal to:
(4) 316
Taking modulus of 4z2 = - z gives 4|z|2 = |z|, so |z| = 0 or |z| = 14.
If |z| = 0, z = 0 is a solution.
If |z| = 14, let z = 14ei ; then 4 116e2i = - 14e-i , so
e3i = -1 = 3, , 5 3 (three distinct values of z)
z S |z|2 = 0 + 3 116 = 316
Answer: (4)
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