jee-main 2014 Q63

jee-main · India · 06apr Complex Numbers Arithmetic Modulus Inequalities and Bounds (Proof-Based)

If $z$ is a complex number such that $| z | \geq 2$, then the minimum value of $\left| z + \frac { 1 } { 2 } \right|$:
(1) Is strictly greater than $\frac { 5 } { 2 }$
(2) Is strictly greater than $\frac { 3 } { 2 }$ but less than $\frac { 5 } { 2 }$
(3) Is equal to $\frac { 5 } { 2 }$
(4) Lies in the interval $( 1,2 )$

If $z$ is a complex number such that $| z | \geq 2$, then the minimum value of $\left| z + \frac { 1 } { 2 } \right|$:\\
(1) Is strictly greater than $\frac { 5 } { 2 }$\\
(2) Is strictly greater than $\frac { 3 } { 2 }$ but less than $\frac { 5 } { 2 }$\\
(3) Is equal to $\frac { 5 } { 2 }$\\
(4) Lies in the interval $( 1,2 )$

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