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The number of values of z (real or compl...

The number of values of z (real or complex) e simultaneously satisfying the system of equations ` 1+z+z^2+z^3+...z^17=0 and 1+z+z^2+z^3+..+z^13=0` is

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Number of values of z (real or complex) simultaneously satisfying the system of equations 1+z+z^(2)+z^(3)++z^(17)=0 and 1+z+z^(2)+z^(3)++z^(13)=0 is

If z and w are two complex numbers simultaneously satisfying te equations,z^(3)+w^(5)=0 and z^(2)+bar(w)^(4)=1, then

Knowledge Check

  • If z_(1) ,z_(2) be two complex numbers satisfying the equation |(z_(1)+z_(2))/(z_(1)-z_(2))|=1 , then

    A
    `z_(1)barz_()+z_(2)barz_(1)=1`
    B
    ` (barz_(1)/( barz_(2))) = - z_(1)/z_(2)`
    C
    `z_(1)barz_(2) +z_(2)barz_(1)=0`
    D
    `Re(z_(1)barz_(2))=0`

  • If z is a complex number satisfying the equaiton z^(6) - 6z^(3) + 25 = 0 , then the value of |z| is

    A
    `5^(1//3)`
    B
    `25^(1//3)`
    C
    `125^(1//3)`
    D
    `625^(1//3)`

  • The two complex numbers satisfying the equation z bar (z) - (1 + i) z - ( 3 + 2 i) bar(z) + ( 1 + 5i) = 0 are

    A
    `1 + i, e - 2i`
    B
    `1 + i, 3 + 2i`
    C
    `1 - i, 3 + 2i`
    D
    `1 - i, 3 - 2i`

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    The number of complex numbers z satisfying |z-2-i|=|z-8+i| and |z+3|=1 is

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