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2021 AMC 12B Question 18

AMC12 · 2021 AMC 12B

Question 18

Let $z$ be a complex number satisfying $12|z|^2$ $=2|z+2|^2+|z^2+1|^2+31.$ What is the value of $z+\dfrac{6}{z}?$
  1. $-2$
  2. $-1$
  3. $\dfrac{1}{2}$
  4. $1$
  5. $4$