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

Let `z in C` and if `A={z:"arg"(z)=pi/4}`and `B={z:"arg"(z-3-3i)=(2pi)/3}`. Then `n(A frown B)=`

A

`1`

B

`2`

C

`3`

D

`0`

Text Solution

Verified by Experts

The correct Answer is:
D
`(d)` `A={z,arg(z)=(pi)/(4)}`
`z` lies on the ray from origin (excluding origin) at an angle `pi//4` with positive real axis.
`B ={z,arg(z-3-3i)=(2pi)/(3)}`
`z` lies on the ray from `3+3i`(excluding `3+3i`) at an angle `2pi//3` with positive real axis.

We can observe that `3+3i in A` but `ne B`
`:.n(AnnB)=0`
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