Complex Numbers
Complex Numbers
Allen Star Batch
Grade 11
Question:
$w_1, w_2$ be roots of $(a+\bar{c})z^2 + (b+\bar{b})z + (\bar{a}+c) = 0$. If $|z_1| < |z_2| < 1$, then
$|w_1| < 1$
$|w_1| = 1$
$|w_2| < 1$
$|w_2| = 1$
Step-by-Step Solution
For a triangle with sides $a, a, b$, the triangle inequality requires $2a > b$, so $b b$ to constrain possible side lengths and count systematically by ranges.
Correct Answer: 2,4