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Question

If Z is a complex number such that |z| greater than or equal to 2, then the minimum value of z+12.

A

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B

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C

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D

Less than

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Solution

The correct option is B


z+12 is the distance of Z from 12.

|z|=2 is a circle with centre as origin and radius 2. |z|2 all the points outside and on the circle

|z| =2.

It is the shaded region in the figure.

The closest point in that region on the negative x-axis, which is (-2,0). So the least distance is 12-(-2)= 32.

Or

Another way of solving is by applying triangle inequality.

z+12|z|12

=2-12
= 32


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