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If (z+1)/(z+i) is a purely imaginary num...

If `(z+1)/(z+i)` is a purely imaginary number (where`(i=sqrt(-1)`), then z lies on a

A

straight line

B

circle

C

circle with radius = `1/sqrt(2)`

D

circle passing through the origin

Text Solution

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The correct Answer is:
B, C, D
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Knowledge Check

  • If the number (z-1)/(z+1) is purely imaginary, then

    A
    `|z|=1`
    B
    `|z| gt 1`
    C
    `|z| lt 1`
    D
    `|z| gt 2`

  • If the ratio (1-z)/(1+z) is purely imaginary, then

    A
    `0 lt |z| lt 1`
    B
    `|z|=1`
    C
    `|z| gt 1`
    D
    bounds for `|z|` can not be decided

  • If the number ( z - 1)/( z + 1) is purely imaginary, then

    A
    `|z| gt 1`
    B
    ` | z | lt 1 `
    C
    ` | z| = 1 `
    D
    `| z| gt 2 `

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