If z=x+i ya n dx^2+y^2=16 , then the ran...

If `z=x+i ya n dx^2+y^2=16 ,` then the range of `||x|-|y||` is `[0,4]` b. `[0,2]` c. `[2,4]` d. none of these

`[0,4]`

`[0,2]`

`[2,4]`

none of these

Text Solution

Verified by Experts

The correct Answer is:

Here `x=4costheta,y=4sintheta`.
`therefore " " ||x|-|y||=|4|costheta|-4 |sintheta|`
`=4||costheta|-|sintheta||`
`=4sqrt(1-2|costheta||sintheta|)`
`=4sqrt(1-|sin2theta|)`
Hence, the range is [0, 4].

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