Complex Numbers & Argand Diagrams (Edexcel A Level Further Maths: Core Pure): Exam Questions

In an Argand diagram, the points  and  are represented by the complex numbers  and  respectively. The points and  are the end points of a diameter of a circle .

Find the equation of  giving your answer in the form 

     , 

The circle , with equation , intersects  at the points representing the complex numbers  and 

Find the complex numbers and 

where  and  are real constants.

Given that  is a root of the equation , show the roots of   on a single Argand diagram.