The correct options are
A maximum value of
|z| is
√8+1 C minimum value of
|z| is
√8−1|z−2+2i|=1 ⇒|z−(2−2i)|=1 ∵||z1|−|z2||≤|z1−z2|≤|z1|+|z2| ⇒||z|−√8|≤1≤|z|+√8 ||z|−√8|≤1 and
1≤|z|+√8 ⇒−1≤|z|−√8≤1 and
|z|≥−√8+1 ⇒√8−1≤|z|≤√8+1 and
|z|≥0 ∴|z|∈[√8−1,√8+1] So, minimum value of
|z| is
√8−1 and maximum value of
|z| is
√8+1 Alternate solution :
|z−(2−2i)|=1 Let,
z=x+iy ⇒(x−2)2+(y+2)2=1 It represents a circle with centre
(2,−2) and radius
1 unit
|z|=|z−0|= distance of point
P(z) from origin
∴(OP)min=OC−r=√8−1 and
(OP)max=OC+r=√8+1