(a)[2]
Find the complex number shown by point $P$. Give your answer in the form $x + iy$, where $x$ and $y$ are exact real values.
(b)[3]
Find the largest possible value of $\arg z$ for points in the shaded region.
Mathematics 9709 · AS & A Level · Complex numbers
Complex numbers — practice question
The shaded part of the Argand diagram, enclosed by a straight line and a circle, shows the complex numbers $z$ for which $\operatorname{Re} z \leq 2$ and $|z - (3 + i)| \leq 2$ hold. The point $P$ marked on the diagram is one of the intersection points of the line and the circle.
Worked solution & mark scheme
This 5-mark question has a full step-by-step worked solution and mark scheme. One marking point: “A full method that leads to an equation in $y$ only, for example $(2-3)^2+(y-1)^2=4$” …
- Full mark scheme, point by point
- Step-by-step worked solution
- Write your answer & get it marked instantly by AI