Originally Posted by

**afeasfaerw23231233** p294 q16 c

given

$\displaystyle z^2-2z+k=0$

.......(*), where k is real, has no real roots.

find , in terms of k, the squares of the roots of (*), expressing the answers in the form x+iy where x and real are real.

as k varies, find the equation of the locus of the pts in the argand plane representing the squares of the roots of (*)

my working:

$\displaystyle z = \frac {2\pm \sqrt{4-4k}}2 = 1 \pm \sqrt{1-k}$

square of the roots$\displaystyle = 2-k \pm 2\sqrt{k-1}i$

don't know how to find the locus. thanks.