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If |z-3+2i|＜=4 then the difference between the greatest and the least value of |z| is : A) 2(13^1/2) B) 8 C) 4+((13)^1/2) D) (13)^1/2

If |z-3+2i|＜=4 then the difference between the greatest and the least value of |z| is :
A) 2(13^1/2)
B) 8
C) 4+((13)^1/2)
D) (13)^1/2

Grade:

2 Answers

kkbisht
90 Points
5 years ago
The inequality  |z-3+2i|\sqrt{}32+22 = \sqrt{}13 and radus is 4 . So any point on the circle( z ) will have maximum distance from origin  (|z| )is 4+\sqrt{}13 and minimum distance will be 4-\sqrt{}13. So the difference is  4+\sqrt{}13 -(4-\sqrt{}13)= 2\sqrt{}13
It is to be understud that |z| represents the distance of any point P(x,y)  represented by complex number  z =x+iy) in the argand plane from the origin
Kushagra Madhukar
askIITians Faculty 628 Points
3 years ago
Dear student,
Please find the answer to your question.
 
The given equation represents the circle with center(3,−2) and is of radius (R)=4
∣z∣ represents the distance of point 'z' from origin
Now, the greatest and least distances occur along  the normal through the origin 
We know, that the Normal always passes through center of circle
Hence least value of |z| = 4 – √13
Max value of |z| = 4 + √13
Hence difference = (4 + √13) – (4 – √13) = 2√13
 
Thanks and regards,
Kushagra

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