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The number of complex numbers z such tha...

The number of complex numbers `z` such that `|z-1|=|z+1|=|z-i|` equals

A

`0`

B

`1`

C

`2`

D

`oo`

Text Solution

Verified by Experts

The correct Answer is:
B
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Knowledge Check

  • If z_(1) and z_(2) are two non-zero complex numbers such that |z_(1)+z_(2)|=|z_(1)|+|z_(2)| , then arg. z_(1)- arg. z_(2) equals :

    A
    `-pi`
    B
    `(pi)/(2)`
    C
    `-(pi)/(2)`
    D
    `0`

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    A
    1)z is a purely imaginary
    B
    2)z is a purely real
    C
    3)Real part of z is the same as its imaginary part
    D
    4)z is any complex number

  • If z is a complex number then

    A
    `|z^(2)|gt|z|^(2)`
    B
    `|z^(2)|=|z|^(2)`
    C
    `|z^(2)|lt|z|^(2)`
    D
    `|z^(2)| ge|z|^(2)`

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