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March 12th, 2019, 03:21 AM   #1
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Complex No. Problem

If |z-2| <= 6 find the greatest value of |z-i| .

I started like this:

Let z = x + iy

|z-2| <= 6 represents all the points inside the circle and on the circumference of the circle (x-2)^2 + y^2 = 36 i.e a circle having center at (2,0) and radius = 6.

How to relate to |z-i|?

Could someone give me a clue?

Last edited by skipjack; March 12th, 2019 at 04:06 AM.
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March 12th, 2019, 04:06 AM   #2
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Starting from the point (0, 1) (representing i), draw a straight line segment that passes through the point P(2, 0) and meets the circle's circumference at point Q. As PQ = 6, what is the answer?
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March 12th, 2019, 04:59 AM   #3
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I do not know the answer . So what should represent the greatest value of |z-i| from the above?
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March 12th, 2019, 07:32 AM   #4
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The distance from (0, 1) to Q, which is the sum of the distance from (0, 1) to P(2, 0) and the distance from P to Q.
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March 12th, 2019, 07:58 AM   #5
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Got it . So max | z -i| = 11. Many thanks
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