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Let z in C and if A={z,arg(z)=(pi)/(4)} ...

Let `z in C` and if `A={z,arg(z)=(pi)/(4)}` and `B={z,arg(z-3-3i)=(2pi)/(3)}`. Then `n(AnnB)` is equal to

A

1

B

2

C

3

D

0

Text Solution

Verified by Experts

The correct Answer is:
D
We observe that arg(z) `=pi//4` is the ray originating from origin making angle `pi//4` with OX. So, A is an infinite set of points lying on this ray. The set B is the set of all points on the ray originating from (3,3) making angle `(2pi//3)` with x-axis as shown in fig. 70. The initial points of these two rays are not included in the two sets .

Hence, `A frown B = phi` and so `n(A frown B)=0`.
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