Complex Numbers 2 Question 7

7. If z is a complex number such that |z|2, then the minimum value of |z+12|

(a) is equal to 5/2

(2014 Main)

(b) lies in the interval (1,2)

(c) is strictly greater than 5/2

(d) is strictly greater than 3/2 but less than 5/2

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Answer:

Correct Answer: 7. (b)

Solution:

  1. |z|2 is the region on or outside circle whose centre is (0,0) and radius is 2 .

Minimum |z+12| is distance of z, which lie on circle |z|=2 from (1/2,0).

Minimum |z+12|= Distance of 12,0 from (2,0)

=2+122+0=32=12+22+0=32

Geometrically Min |z+12|=AD

Hence, minimum value of |z+12| lies in the interval (1,2).



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