A theorem of Cauchy states that all the roots of the equation $z^n+a_1 z^{n-1}+a_2 z^{n-2}+\cdots+a_n=0$, where $a_1, a_2, \ldots, a_n$ are real, lie inside the circle $|z|=1+\max \left\{a_1, a_2, \ldots, a_n\right\}$, i.e. $|z|=1$ plus the maximum of the values $a_1, a_2, \ldots, a_n$. Verify this theorem for the special cases
(a) $z^3-z^2+z-1=0$,
(b) $z^4+z^2+1=0$,
(c) $z^4-z^2-2 z+2=0$,
(d) $z^4+3 z^2-6 z+10=0$.