Paper 3 May/June 2010 MATHEMATICS (9709/32) A Levels
لطفا برای اطمینان از عملکرد و تجربه بهتر از مرورگرهای مدرن و به روز مانند کروم یا فایرفاکس استفاده کنید.

a) The equation $2{x^3} - {x^2} + 2x + 12 = 0$ has one real root and two complex roots. Showing your working, verify that $1 + i{\text{ }}\surd 3$ is one of the complex roots. State the other complex root.
b) On a sketch of an Argand diagram, show the point representing the complex number $1 + i{\text{ }}\surd 3$
On the same diagram, shade the region whose points represent the complex numbers $z$ which atisfy both the inequalities $\left| {z - 1 - i{\text{…