Q11 (d) (ii)

Criteria	Marks
Provides correct answers	2
Uses the quadratic formula to obtain $z=-1\pm\sqrt{-i}$, or equivalent merit	1

Sample answer:

$z^2+2z+1+i=0$
$z=\frac{-2\pm\sqrt{(2)^2-4(1)(1+i)}}2$
$=\frac{-2\pm2\sqrt{1-1-i}}2=-1\pm\sqrt{-i}$

From part (i):

$z=-1+\frac1{\sqrt2}-\frac{i}{\sqrt2}\quad\text{or}\quad z=-1-\frac1{\sqrt2}+\frac{i}{\sqrt2}$

that is,

$z=\frac{1-\sqrt2}{\sqrt2}-\frac1{\sqrt2}i\quad\text{or}\quad z=-\frac{1+\sqrt2}{\sqrt2}+\frac1{\sqrt2}i$