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Offline Priya

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Needs help with complex numbers
« 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!
« Last Edit: June 18, 2009, 04:02:22 am by Priya »
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Offline astarmathsandphysics

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Re: Needs help with complex numbers
« Reply #1 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
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Offline astarmathsandphysics

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Re: Needs help with complex numbers
« Reply #2 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
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