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 March 12th, 2019, 03:21 AM #1 Member   Joined: Jul 2017 From: KOLKATA Posts: 38 Thanks: 2 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.
 March 12th, 2019, 04:06 AM #2 Global Moderator   Joined: Dec 2006 Posts: 20,632 Thanks: 2080 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?
 March 12th, 2019, 04:59 AM #3 Member   Joined: Jul 2017 From: KOLKATA Posts: 38 Thanks: 2 I do not know the answer . So what should represent the greatest value of |z-i| from the above?
 March 12th, 2019, 07:32 AM #4 Global Moderator   Joined: Dec 2006 Posts: 20,632 Thanks: 2080 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.
 March 12th, 2019, 07:58 AM #5 Member   Joined: Jul 2017 From: KOLKATA Posts: 38 Thanks: 2 Got it . So max | z -i| = 11. Many thanks

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