If z is a complex number such that |z| geqsla | vedclass

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(A) Given $|z| \geqslant 2$. We want to find the minimum value of $|z + \frac{1}{2}|$. By the triangle inequality,we know that $|z + w| \geqslant ||z|

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equal to $\frac{3}{2}$

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(A) Given $|z| \geqslant 2$. We want to find the minimum value of $|z + \frac{1}{2}|$. By the triangle inequality,we know that $|z + w| \geqslant ||z| - |w||$. Here,$|z + \frac{1}{2}| \geqslant ||z| - |-\frac{1}{2}|| = ||z| - \frac{1}{2}|$. Since $|z| \geqslant 2$,the expression $|z| - \frac{1}{2}$ is at least $2 - \frac{1}{2} = \frac{3}{2}$. Thus,$|z + \frac{1}{2}| \geqslant \frac{3}{2}$. The minimum value is $\frac{3}{2}$ when $z$ is a real number such that $z = -2$.

If $z$ is a complex number such that $|z| \geqslant 2$,then the minimum value of $|z + \frac{1}{2}|$ is:

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