# MIE 2016/Day 1/Problem 3

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### Problem 3

Let $Z_1$ and $Z_2$ be complex numbers such that $Z_2$ is a pure imaginary number and $|Z_1-Z_2|=|Z_2|$. For any values of $Z_1$ and $Z_2$ that satisfies these conditions we have:

(a) $\mbox{Im}(Z_2)>0$

(b) $\text{Im}(Z_2)\leq0$

(c) $|Z_1|\leq2|Z_2|$

(d) $\text{Re}(Z_1)\geq0$

(e) $\text{Re}(Z_1)\geq\text{Im}(Z_2)$