Complex NumbersHard
Question
If |z1 - 1| < 1, |z2 - 2| < 2, |z3 - 3| < 3, then |z1 + z2 + z3|
Options
A.is less than 6
B.is more than 3
C.is less than 12
D.lies between 6 and 12
Solution
|(z1 - 1) + (z2 - 2) + (z3 - 3)| ≤ |z1 - 1| + |z2 - z| + |z3 - 3|
⇒ |z1 + z2 + z3 - 6| < 6
Let z = z1 + z2 + z3 = 3
then |z - 6| < 6 is circular disc
Clearly |z| < 12
⇒ |z1 + z2 + z3 - 6| < 6
Let z = z1 + z2 + z3 = 3
then |z - 6| < 6 is circular disc
Clearly |z| < 12
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