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If arg ((z(1) -(z)/(|z|))/((z)/(|z|))) =...

If arg `((z_(1) -(z)/(|z|))/((z)/(|z|))) = (pi)/(2) and |(z)/(|z|)-z_(1)|=3`, then `|z_(1)|` equals to a. `sqrt(3)` b. `2sqrt(2)` c. `sqrt(10)` d. `sqrt(26)`

A

`sqrt(26)`

B

`sqrt(10)`

C

`sqrt(3)`

D

`2sqrt(2)`

Text Solution

Verified by Experts

The correct Answer is:
B
Given that
`arg((z_(1)-(z)/|z_(1)|)/((z)/(|z|))) = (pi)/(2) `

and `|(z)/|z|-z_(1)|=3`
form which we can estabish the above gemoetry
form the diagram.
`|z_(1)| = sqrt(9+1)= sqrt(10)`
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