Complex Numbers
Algebra of Complex Numbers
Grade Class 11
Question:
<p>If \( z \) simultaneously satisfies \( 3(z-12) = 5(z(z-9)) \), which of the following hold?</p>
\(\text{Re}(z) > 0\)
\(\text{Im}(z) > 0\)
\(|z| < 2\)
\(z\) lies in the second quadrant
Step-by-Step Solution
Key Concept: Solve the equation for z; check real/imaginary parts and modulus.
<p>From the given equation, compute $z$, then verify which conditions hold. The solutions yield $\text{Re}(z) < 0$ and $\text{Im}(z) > 0$, confirming C and D.</p>
Correct Answer: CD