If $z$ is a complex number such that $|z|\geq\,2$, then the minimum value of $ |z + (1/2) | $
Updated On: Jul 6, 2022
is strictly greater than $5/2$
is strictly greater than $3/2$ but less than $5/2$
is equal to $5/2$
lies in the interval $(1, 2)$.
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The Correct Option isD
Solution and Explanation
$|z| \ge 2$ is the region lying on or outside the circle with centre $(0,0)$ and radius $2$.
$\left|z+\frac{1}{2}\right|$ is the distance of $'z'$ from $\left(-\frac{1}{2}, 0\right)$ which lies inside the circle.
$\therefore$ min. $\left|z+\frac{1}{2}\right| =$ distance of $\left(-\frac{1}{2}, 0\right)$ from
$\left(-2, 0\right)=\frac{3}{2} \in\left(1, 2\right)$
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Top Questions on Complex Numbers and Quadratic Equations
Complex Number: Any number that is formed as a+ib is called a complex number. For example: 9+3i,7+8i are complex numbers. Here i = -1. With this we can say that i² = 1. So, for every equation which does not have a real solution we can use i = -1.
Quadratic equation: A polynomial that has two roots or is of the degree 2 is called a quadratic equation. The general form of a quadratic equation is y=ax²+bx+c. Here a≠0, b and c are the real numbers.
