Math

If z is a non-real complex number and z^2−26z is a real number, what is the value of z+z¯?


z¯ denotes the conjugate of the complex number z.

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asked by Crow
  1. Let z=a+bi where i²=-1
    then
    z²-26z
    =-b²-26a + (2a-26)bi
    Since is real, and z is non-real,
    therefore b≠0, and consequently
    (2a-26)bi = 0
    =>
    2a-26=0,
    =>
    a=13

    Thus z=13+bi, z(conjugate) = 13-bi
    so
    z+z(conjugate)=13+bi+13-bi=26

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    posted by MathMate

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