3
Question
Let z1,z2 be two complex numbers represented by points on the circle |z|=1 and |z|=2 respectively then
Let z1,z2 be two complex numbers represented by points on the circle |z|=1 and |z|=2 respectively then
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Solution
The correct options are
A max|2z1+z2|=4
B min|z1−z2|=1
C ∣∣∣z2+1z1∣∣∣≤3
The equations are that of circles with center at the origin and radius 1 and 2 units respectively.
Max|2z1+z2|=2|z1|+|z2|=2×1+2=4
Min|z1−z2|=|z2|−|z1|=2−1=1
Max|z2+1z1|=|z2|+Max(1|z1|)=2+1=3
Hence, (a), (b), (c) are correct.
A max|2z1+z2|=4
B min|z1−z2|=1
C ∣∣∣z2+1z1∣∣∣≤3
The equations are that of circles with center at the origin and radius 1 and 2 units respectively.
Max|2z1+z2|=2|z1|+|z2|=2×1+2=4
Min|z1−z2|=|z2|−|z1|=2−1=1
Max|z2+1z1|=|z2|+Max(1|z1|)=2+1=3
Hence, (a), (b), (c) are correct.
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