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March 12th, 2019, 03:21 AM  #1 
Member Joined: Jul 2017 From: KOLKATA Posts: 46 Thanks: 2  Complex No. Problem
If z2 <= 6 find the greatest value of zi . I started like this: Let z = x + iy z2 <= 6 represents all the points inside the circle and on the circumference of the circle (x2)^2 + y^2 = 36 i.e a circle having center at (2,0) and radius = 6. How to relate to zi? 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: 20,919 Thanks: 2203 
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: 46 Thanks: 2 
I do not know the answer . So what should represent the greatest value of zi from the above?

March 12th, 2019, 07:32 AM  #4 
Global Moderator Joined: Dec 2006 Posts: 20,919 Thanks: 2203 
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: 46 Thanks: 2 
Got it . So max  z i = 11. Many thanks


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