Question

For all complex numbers $z_1,z_2$ satisfying $|z_1|=12$ and $|z_2–3–4i|=5$, then find the minimum value of $|z_1–z_2|$.

• A. 1
• B. 2
• C. 5
• D. 4

Answer 1

The correct option is B 2

$|z_1–z_2|=|z_1–(z_2–3–4i)–(3+4i)|$
$\ge |z_1|–|z_2–3–4i|–|3+4i|$
$\ge 12–5–5$
$\ge 2$