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For the real parameter t,the locus of th...

For the real parameter t,the locus of the complex number `z=(1-t^2)+isqrt(1+t^2)` in the complex plane is

A

`pi//6`

B

`5pi//12`

C

`7pi//12`

D

`11pi//12`

Text Solution

Verified by Experts

The correct Answer is:
B
`(b)` `z^(4)=2(1-sqrt(3)i)=4((1)/(2)-(sqrt(3))/(2)i)`
`=4[cos(-(pi)/(3))+isin(-(pi)/(3))]`
`z=sqrt(2)[cos"(2mpi-(pi//3))/(4)+isin"(2mpi-(pi//3))/(4)]`
For `m=1`, `z=sqrt(2)[cos((5pi)/(12))+isin((5pi)/(12))]`
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