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Question

If |z2+2i|=1, then

A
maximum value of |z| is 8+1
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B
maximum value of |z| is 10+1
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C
minimum value of |z| is 81
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D
minimum value of |z| is 61
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Solution

The correct options are
A maximum value of |z| is 8+1
C minimum value of |z| is 81
|z2+2i|=1
|z(22i)|=1
||z1||z2|||z1z2||z1|+|z2|
||z|8|1|z|+8
||z|8|1 and 1|z|+8
1|z|81 and |z|8+1
81|z|8+1 and |z|0
|z|[81,8+1]
So, minimum value of |z| is 81
and maximum value of |z| is 8+1

Alternate solution :


|z(22i)|=1
Let, z=x+iy
(x2)2+(y+2)2=1
It represents a circle with centre (2,2) and radius 1 unit

|z|=|z0|= distance of point P(z) from origin
(OP)min=OCr=81
and (OP)max=OC+r=8+1

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