## Yahoo! Group Title 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? one year ago one year ago

1. mukushla Group Title

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

2. Yahoo! Group Title

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

3. mukushla Group Title

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

4. Yahoo! Group Title

Why? 2xy + y =0

5. mukushla Group Title

because a is a real number

6. Yahoo! Group Title

got it.....

7. mukushla Group Title

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

8. mukushla Group Title

do u know why $$y\neq0$$

9. Yahoo! Group Title

if y=0 then imaginary part becomes 0

10. mukushla Group Title

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

11. Yahoo! Group Title

yes

12. mukushla Group Title

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