Art of Problem Solving
AoPS Online
Math texts, online classes, and more
for students in grades 5-12.
Visit AoPS Online ‚
Books for Grades 5-12 Online Courses
Beast Academy
Engaging math books and online learning
for students ages 6-13.
Visit Beast Academy ‚
Books for Ages 6-13 Beast Academy Online
AoPS Academy
Small live classes for advanced math
and language arts learners in grades 2-12.
Visit AoPS Academy ‚
Find a Physical Campus Visit the Virtual Campus

MIE 2016/Day 1/Problem 3

Revision as of 21:41, 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...")
(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)

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

Retrieved from "https://artofproblemsolving.com/wiki/index.php?title=MIE_2016/Day_1/Problem_3&oldid=89569"