## anonymous 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?

1. anonymous

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

2. anonymous

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

3. anonymous

$$y\neq0$$ and$2xy+y=0$right?

4. anonymous

Why? 2xy + y =0

5. anonymous

because a is a real number

6. anonymous

got it.....

7. anonymous

2xy+y=0 and $$y\neq0$$ so$2x+1=0$

8. anonymous

do u know why $$y\neq0$$

9. anonymous

if y=0 then imaginary part becomes 0

10. anonymous

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

11. anonymous

yes

12. anonymous

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