First slide

Operations on Sets

Question

If $A = {z : (1 + 2 i) \bar{z} + (1 - 2 i) z + 2 = 0}$ and $B = {z : (3 + 2 i) \bar{z} + (3 - 2 i) z + 3 = 0}$ then

Moderate

A

$A \cap B$ is a singleton set
B

$A \subseteq B$
C

$B \subseteq A$
D

$A \cap B = ϕ$

Solution

Equations in sets $A$ and $B$ represent straight
line with ${\bar{α}}_{1} = 1 + 2 i$ and ${\bar{α}}_{2} = 3 + 2 i$ Since $\frac{{\bar{α}}_{1}}{α_{1}} \neq \frac{{\bar{α}}_{2}}{α_{2}}$ so the
lines are intersecting, hence $A \cap B$ is a singleton set.

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