Show that 4+i and -4-i are the sqaure rooots of 15 +8i
It is sufficient to show that
$\displaystyle (4+i)^2=15+8i$
and that:
$\displaystyle (-4-i)^2=15+8i$
to show that $\displaystyle 4+i$ and $\displaystyle -4-i$ are square roots of $\displaystyle 15+8i$. (In fact it is sufficent to show that one of these is a square root since the other is minus one times it, and so also of necessity a square root of $\displaystyle 15+8i$)
RonL