Always positive integer

Algebra Level 4

If ∣ z − i ∣ < 1 |z-i|<1 , then ∣ z + 12 + 6 i ∣ |z+12+6i| is always:

greater than 15 less than 15 greater than 13 less than 13

A Former Brilliant Member by A Former Brilliant Member

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1 solution

For the Absolute value z-i = 1 then z+12+6i=0 putting the i value i = 1+z will get the z = -0.8571 then it will be in put in previous equation 1 in out of modules it become positive integer which is greater than 1 1.857<1 ,then absolute value is 14.7151 which is greater than 14 so answer will be greater than 14

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∣ z − i ∣ < 1 |z-i|<1 means a complex no. z z lies inside the circle of radius one unit centred at ( 0 , 1 ) (0,1) in Argand's Plane. So, ∣ z + 12 + 6 i ∣ |z+12+6i| will have range ( 1 2 2 + 7 2 − 1 , 1 2 2 + 7 2 + 1 ) (\sqrt{12^2+7^2}-1,\sqrt{12^2+7^2}+1) = ( 12.89244 , 14.89244 ) (12.89244,14.89244) .

A Former Brilliant Member - 4 years, 9 months ago

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