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

(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

(2014 Main)

Show Answer

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

alt text

Geometrically Min |z+12|=AD

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

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