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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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mukushla
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z=x+iy
evaluate the value of a in terms of x and y

Yahoo!
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x^2 + 2xiy  y^2 + x + iy + 1 = a

mukushla
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\(y\neq0\)
and\[2xy+y=0\]right?

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Why? 2xy + y =0

mukushla
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because a is a real number

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got it.....

mukushla
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2xy+y=0 and \(y\neq0\) so\[2x+1=0\]

mukushla
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do u know why \(y\neq0\)

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if y=0 then imaginary part becomes 0

mukushla
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\[x=\frac{1}{2}\]so a becomes\[a=\frac{3}{4}y^2\]am i right?

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yes

mukushla
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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 :)