Assertion (A): If z is a complex number such | vedclass

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(D) For the Assertion $(A)$: Given $|z| \geq 3$.We use the inequality $|z_1 + z_2| \geq ||z_1| - |z_2||$.Thus,$|z + \frac{3}{z}| \geq ||z| - |\frac{3}

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$A$ is false but $R$ is true.

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(D) For the Assertion $(A)$: Given $|z| \geq 3$.We use the inequality $|z_1 + z_2| \geq ||z_1| - |z_2||$.Thus,$|z + \frac{3}{z}| \geq ||z| - |\frac{3}{z}|| = ||z| - \frac{3}{|z|}||$.Let $f(t) = t - \frac{3}{t}$ where $t = |z| \geq 3$.Since $f(t)$ is an increasing function for $t \geq 3$,the minimum value occurs at $t = 3$.$f(3) = 3 - \frac{3}{3} = 3 - 1 = 2$.So,$|z + \frac{3}{z}| \geq 2$.The assertion states the least value is $1$,which is false.For the Reason $(R)$: The triangle inequality states $|z_1 + z_2| \leq |z_1| + |z_2|$. The statement $|z_1 - z_2| \leq |z_1| + |z_2|$ is also a valid form of the triangle inequality,which is true.Therefore,$A$ is false but $R$ is true.

Assertion $(A)$: If $z$ is a complex number such that $|z| \geq 3$,then the least value of $|z + \frac{3}{z}|$ is $1$.
Reason $(R)$: $|z_1 - z_2| \leq |z_1| + |z_2|$,for any two complex numbers $z_1, z_2$.
The correct option among the following is:

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Assertion $(A)$: If $z$ is a complex number such that $|z| \geq 3$,then the least value of $|z + \frac{3}{z}|$ is $1$.Reason $(R)$: $|z_1 - z_2| \leq |z_1| + |z_2|$,for any two complex numbers $z_1, z_2$.The correct option among the following is: