Question

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?

Answer 1

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

Answer 2

x^2 + 2xiy - y^2 + x + iy + 1 = a

Answer 3

\(y\neq0\)

and\[2xy+y=0\]right?

Answer 4

Why? 2xy + y =0

Answer 5

because a is a real number

Answer 6

got it.....

Answer 7

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

Answer 8

do u know why \(y\neq0\)

Answer 9

if y=0 then imaginary part becomes 0

Answer 10

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

Answer 11

yes

Answer 12

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