Paper 3 October/November 2008 MATHEMATICH (9709/3) A Levels
لطفا برای اطمینان از عملکرد و تجربه بهتر از مرورگرهای مدرن و به روز مانند کروم یا فایرفاکس استفاده کنید.

a) The complex number $u$ is defined by $u = \frac{5}{{\alpha + 2i}}$, where the constant $\alpha $ is real.
(i) Express $u$ in the form $x + iy$, where $x$ and $y$ are real.
(ii) Find the value of $\alpha $ for which arg $\left( u \right) = \frac{3}{4}\pi $, where $u$ denotes the complex conjugate of $u$.
b) On a sketch of an Argand diagram, shade the region whose points represent complex numbers $z$ which satisfy both the inequalities…