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Let z be a complex number such that |z...

Let z be a complex number such that ` |z| + z = 3 + I " (where I " = sqrt(-1)) ` . Then |z| is equal to :

A

`5/3`

B

`5/4`

C

`( sqrt34)/(3)`

D

`(sqrt41)/(4)`

Text Solution

Verified by Experts

The correct Answer is:
A
Let `z=x + iy`
`therefore sqrt(x ^(2) + y^(2))+ x+iy =3 +i implies " " sqrt(x ^(2) + y ^(2)) + x=3" "...(i)`
And `y =1`
`therefore ` From (i) `sqrt(x ^(2) +1 ) =3 -x implies " "x=4/3" " therefore z = 4/3 + i implies |z| =5/3`
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