Paper 3 October/November 2011 MATHEMATICS (9709/33) A Levels
لطفا برای اطمینان از عملکرد و تجربه بهتر از مرورگرهای مدرن و به روز مانند کروم یا فایرفاکس استفاده کنید.

a) Showing your working, find the two square roots of the complex number $1 - \left( {2{\text{ }}\surd 6} \right)i$. Give your answers in the for $x + iy$, where x and y are exact.
b) On a sketch of an Argand diagram, shade the region whose points represent the complex number $z$ which satisfy the inequality $\left| {z - 3i} \right| \leqslant 2$. Find the greatest value of arg $z$ for points in this region.