IGCSE/GCSE/O & A Level/IB/University Student Forum

Qualification => Subject Doubts => GCE AS & A2 Level => Math => Topic started by: Priya on June 18, 2009, 03:46:48 am

Title: Needs help with complex numbers
Post by: Priya on June 18, 2009, 03:46:48 am: Can you explain how to do the last part...

At the same time, I would be really grateful if you could explain how do do maximum of z, least argument and maximum argument...

Thank you very much for all the help!
Title: Re: Needs help with complex numbers
Post by: astarmathsandphysics on June 18, 2009, 08:32:34 am: $z=\frac{3+i}{2-i}=\frac{3+i}{2-i}*\frac{2+i}{2+i}=\frac{5+5i}{5}=1+i$

Minimum of |z-(i+i)|=d-r where d is the distance of the centre of the circle from the origin and r is the radius=1

d= $sqrt(2)$
so ans $sqrt(2)-1$
Title: Re: Needs help with complex numbers
Post by: astarmathsandphysics on June 18, 2009, 08:46:26 am: Maximum value of z=greatest distance from origin. There is usually some trickery involved. In this case it is distance of centre of circle from origin +radius of circle.

Greatest argument is biggest angle that the locus makes with the x axis when you go anticlockwise from the positive x axis. In this case the maximum argument is pi/2 and the minimum argument is 0