If $$A={z$$:$$(1+2i)z$$¯$$+(1$$−$$2i)z+2=0}$$ and $$B={z$$:$$(3+2i)z$$¯$$+(3$$−$$2i)z+3=0}$$ then

Correct option is 1A∩B is a singleton set

Questions

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

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A∩B is a singleton set

A⊆B

B⊆A

A∩B=ϕ

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detailed solution

Correct option is A

Equations in sets A and B represent straightline with α¯1=1+2i and α¯2=3+2i Since α¯1α1≠α¯2α2 so thelines are intersecting, hence A∩ B is a singleton set.

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If A={z:(1+2i)z¯+(1−2i)z+2=0} and B={z:(3+2i)z¯+(3−2i)z+3=0} then

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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