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MIE 2016/Day 1/Problem 3

Revision as of 20:41, 7 January 2018 by Anishanne (talk | contribs) (Created page with "===Problem 3=== Let <math>Z_1</math> and <math>Z_2</math> be complex numbers such that <math>Z_2</math> is a pure imaginary number and <math>|Z_1-Z_2|=|Z_2|</math>. For any va...")
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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) $\text{Re}(Z_1)\geq\text{Im}(Z_2)$


Solution

See Also

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