# Mod Z

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#1
How do we get the least value and great values? I usually use this method to find the minimum and max values of mod z. But here since the origin is the center I couldn’t apply that method. Thank you!!
Last edited by Eris13696; 4 days ago
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4 days ago
#2
(Original post by Eris13696)
How do we get the least value and great values? I usually use this method to find the minimum and max values of mod z. But here since the origin is the center I couldn’t apply that method. Thank you!!
The last picture is not appropriate to this question. |z| just represents the distance of a complex number from the origin. The min and max values in the shaded region should need no working, hence the "write down", but if you can't see this, just pick a couple of points in the shaded region. Can you pick points which are closer or further away from the origin while still in the shaded region.
Last edited by mqb2766; 4 days ago
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#3
(Original post by mqb2766)
The last picture is not appropriate to this question. |z| just represents the distance of a complex number from the origin. The min and max values in the shaded region should need no working, hence the "write down", but if you can't see this, just pick a couple of points in the shaded region. Can you pick points which are closer or further away from the origin while still in the shaded region.
Oh the last picture was just showing the method I use usually, so just to make sure if I have a flaw in it, it’s form a diff question. Oh so I can choose any values here? That’s great to know thank you!!
0
4 days ago
#4
(Original post by Eris13696)
Oh the last picture was just showing the method I use usually, so just to make sure if I have a flaw in it, it’s form a diff question. Oh so I can choose any values here? That’s great to know thank you!!
If you have to choose the smallest value of |z|, then you're meant to consider all possible z and choose the one which has the smallest length or distance from the origin.

In the third picture, they do exactly this, but some simple geometry means that the min and max values of |z| will lie on the extended line segment connecting the origin to the circle centre. In this question, becauses the orign lies in the circle, that geometry does not apply but its simpler.
Last edited by mqb2766; 4 days ago
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