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Yahoo!

  • 3 years ago

Let z be a complex number such that imaginary part of z is non zero and a=z^2+z+1 is real then a cannot take the value?

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  1. mukushla
    • 3 years ago
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    z=x+iy evaluate the value of a in terms of x and y

  2. Yahoo!
    • 3 years ago
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    x^2 + 2xiy - y^2 + x + iy + 1 = a

  3. mukushla
    • 3 years ago
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    \(y\neq0\) and\[2xy+y=0\]right?

  4. Yahoo!
    • 3 years ago
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    Why? 2xy + y =0

  5. mukushla
    • 3 years ago
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    because a is a real number

  6. Yahoo!
    • 3 years ago
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    got it.....

  7. mukushla
    • 3 years ago
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    2xy+y=0 and \(y\neq0\) so\[2x+1=0\]

  8. mukushla
    • 3 years ago
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    do u know why \(y\neq0\)

  9. Yahoo!
    • 3 years ago
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    if y=0 then imaginary part becomes 0

  10. mukushla
    • 3 years ago
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    \[x=-\frac{1}{2}\]so a becomes\[a=\frac{3}{4}-y^2\]am i right?

  11. Yahoo!
    • 3 years ago
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    yes

  12. mukushla
    • 3 years ago
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    so whats the value that a can not take considering \(y\neq0\) clearly\[a\neq\frac{3}{4}\]we are done :)

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