anonymous
  • anonymous
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?
Mathematics
schrodinger
  • schrodinger
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anonymous
  • anonymous
z=x+iy evaluate the value of a in terms of x and y
anonymous
  • anonymous
x^2 + 2xiy - y^2 + x + iy + 1 = a
anonymous
  • anonymous
\(y\neq0\) and\[2xy+y=0\]right?

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anonymous
  • anonymous
Why? 2xy + y =0
anonymous
  • anonymous
because a is a real number
anonymous
  • anonymous
got it.....
anonymous
  • anonymous
2xy+y=0 and \(y\neq0\) so\[2x+1=0\]
anonymous
  • anonymous
do u know why \(y\neq0\)
anonymous
  • anonymous
if y=0 then imaginary part becomes 0
anonymous
  • anonymous
\[x=-\frac{1}{2}\]so a becomes\[a=\frac{3}{4}-y^2\]am i right?
anonymous
  • anonymous
yes
anonymous
  • anonymous
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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