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Let z and w be non - zero complex number...

Let z and w be non - zero complex numbers such that `zw=|z^(2)|` and `|z-barz|+|w+barw|=4.` If w varies, then the perimeter of the locus of z is

A

rectangle

B

square

C

rhombus

D

trapezium

Text Solution

Verified by Experts

The correct Answer is:
B
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Knowledge Check

  • If omega is any complex number such that z omega=|z|^(2) and |z-barz|+|omega+baromega|=4 , then as omega varies, then the area bounded by the locus of z is

    A
    `4` sq. units
    B
    `8` sq. units
    C
    `16` sq. units
    D
    `12` sq. units

  • Let Z and w be two complex number such that |zw|=1 and arg(z)-arg(w)=pi/2 then

    A
    `zoverline(w)=-i`
    B
    `zoverline(w)=i`
    C
    `zoverline(w)=(1-i)/(sqrt(2))`
    D
    `zoverline(w)=(1+i)/(sqrt(2))`

  • Let z and w be two non-zero complex numbers such that | z| = |w| and Arg z + Arg z + Arg w = pi . Then z in terms of w is

    A
    w
    B
    `-w`
    C
    `bar(w)`
    D
    `-bar(w)`

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