If z is a complex number such that |z| ge 2,t | vedclass

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(D) Given $|z| \ge 2$,which represents the region on or outside the circle with center $(0, 0)$ and radius $2$. The expression $|z + \frac{1}{2}|$ rep

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in the interval $(1, 2)$

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(D) Given $|z| \ge 2$,which represents the region on or outside the circle with center $(0, 0)$ and radius $2$. The expression $|z + \frac{1}{2}|$ represents the distance between the complex number $z$ and the point $-\frac{1}{2}$. To find the minimum value of $|z - (-\frac{1}{2})|$,we consider the distance from the point $-\frac{1}{2}$ to the boundary of the circle $|z| = 2$. The distance from the origin $(0, 0)$ to the point $-\frac{1}{2}$ is $\frac{1}{2}$. Since the point $-\frac{1}{2}$ lies inside the circle $|z| = 2$,the minimum distance from the point $-\frac{1}{2}$ to any point $z$ on the circle $|z| = 2$ is given by $R - d$,where $R = 2$ is the radius and $d = \frac{1}{2}$ is the distance from the origin to the point $-\frac{1}{2}$. Minimum value = $2 - \frac{1}{2} = \frac{3}{2}$. Since $\frac{3}{2} = 1.5$,which lies in the interval $(1, 2)$,the correct option is $D$.

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

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