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4-1.Complex numbers
hard
Let $Z_1$ and $Z_2$ be any two complex number.
Statement $1:$ $\left| {{Z_1} - {Z_2}} \right|\, \ge \left| {{Z_{_1}}} \right|\, - \,\left| {{Z_{_2}}} \right|$
Statement $2:$ $\left| {{Z_1} + {Z_2}} \right|\, \le \left| {{Z_{_1}}} \right|\, + \,\left| {{Z_{_2}}} \right|$
A
Statement $1$ is true, Statement $2$ is true,
Statement $2$ is a correct explanation of Statement $1$.
B
Statement $1$ is true, Statement $2$ is true,
Statement $2$ is not a correct explanation of Statement $1.$
C
Statement $1$ is true, Statement $2$ is false
D
Statement $1$ is false, Statement $2$ is true.
(AIEEE-2012)
Solution
Statement $- 1$ and $2$ both are true. It is fundamental property.
But Statement $- 2$ is not correct explanation for Statement $- 1.$
Standard 11
Mathematics
