Use polar forms, arguments and complex multiplication geometry
Find the indicated integer power exactly, together with its modulus and principal argument
\[z=((1)\sqrt{3})+(-1)i,\qquad z^{-1}\]
Write the Cartesian result as
\[a\sqrt{d}+(b\sqrt{e})i\]
with positive square-free radicands. Use radicand 1 for a rational component, including zero
Use the principal argument
\[-\pi<\operatorname{Arg}(z)\leq\pi\]
Enter defined=1 when the argument exists, or defined=0 for zero; enter angle coefficient 0 as a placeholder only when undefined