TS EAMCET · Maths · Complex Number
Assertion (A) If \(z\) is a complex number such that \(|z| \geq 3\), then the least value of \(\left|z+\frac{3}{z}\right|\) is 1 .Reason (R) \(\left|z_1-z_2\right| \leq\left|z_1\right|+\left|z_2\right|\), for any two complex numbers \(z_1, z_2\) The correct option among the following is
- A (A) is true, (R) is true and (R) is the correct explanation for (A).
- B (A) is true, (R) is true but \((R)\) is not the correct explanation for \((A)\)
- C \((A)\) is true but \((R)\) is false.
- D (A) is false but \((R)\) is true.
Answer & Solution
Correct Answer
(D) (A) is false but \((R)\) is true.
Step-by-step Solution
Detailed explanation
We have, \(|z| \geq 3\) Then, \(\left|z+\frac{3}{z}\right| \leq|z|+\left|\frac{3}{z}\right|=\left|z+\frac{3}{z}\right| \leq 3+\left|\frac{3}{z}\right|\) \(\therefore\) Least value of \(\left|z+\frac{3}{z}\right|\) is not 1 And…
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