Complex Numbers
Argument of $z_3$; right-angled triangle in Argand plane
MJMT_Full_Test_07
Grade 12
Question:
Let $z_1=3+3i$, $z_2=9-6\sqrt2+(6\sqrt2-3)i$, $\triangle ABC$ right-angled at $C$. Min and max possible values of $\arg(z_3)$ are $a,b$ ($\arg z_3\in(-\pi,\pi]$). Then $b-a=\dfrac{\pi}{k}$. Find $k$.
Step-by-Step Solution
Key Concept: $C$ lies on circle with diameter $AB$ (right angle at $C$). Find the arc, compute range of $\arg(z_3)$, find $b-a$.
$k=4$.
Correct Answer: 4