SOLUTION: if modulus of (z-1)is less than 3 then prove that modulus of (iz+3-5i)is less than 8?

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Question 54051: if modulus of (z-1)is less than 3 then prove that modulus of (iz+3-5i)is less than 8?
Found 2 solutions by venugopalramana, srimankumar45:
Answer by venugopalramana(3286) About Me  (Show Source):
You can put this solution on YOUR website!
I DONT THINK THAT THE PROBLEM IS CORRECT.PLEASE CHECK
WE HAVE THE FORMULAE
CONSIDER Z=-2..LIMITING CASE(ACTUALLY TAKE Z=-1.9999)
THEN Z-1=-2.999
|Z-1|<3..IT SATISFIES THE GIVEN CONDITION.
NOW CHECK
|IZ+3-5I|=|-2.999I+3-5I|=|3-7.999I|=SQRT(73)>8...SO PLEASE CHECK

Answer by srimankumar45(2) About Me  (Show Source):
You can put this solution on YOUR website!
|z-1|<3
|iz+3-5i|=|i||iz+3-5i|=|-z+3i+5|
=|(4+3i)-(z-1)|
Now
|(4+3i)-(z-1)|<||4+3i|+|z-1||

|iz+3-5i|<|5+3|
<8.
Proved by sriman kumar