Complex Numbers
Match the Following
MMTS_Full_Test_17
Grade 12
Question:
Match List-I with List-II (for $z=x+iy$, $x,y\in\mathbb{R}$): P) Area of triangle formed by $z,\omega z,z+\bar{\omega}z$ is $16\sqrt{3}$ then $|z|$; Q) Area of locus of $z$ if $|\text{Re}\,z|+|\text{Im}\,z|=3$; R) If $|z+6/z|=5$ then maximum of $|z|$; S) Number of complex numbers $z$ satisfying $z^2=\bar{z}$
P-1, Q-4, R-2, S-3
P-2, Q-4, R-3, S-1
P-2, Q-3, R-2, S-1
P-4, Q-3, R-1, S-2
Step-by-Step Solution
Key Concept: Use formulas for equilateral triangle, square area, and complex equation
P→2: $|z|=4$, Q→4: area=18, R→3: max $|z|=6$, S→1: 4 solutions. Match: P-2, Q-4, R-3, S-1.
Correct Answer: 2