# If z is a complex number such that    then the minimum value of    Option 1) is strictly greater than Option 2) is strictly greater than   but less than Option 3) is equal to  Option 4) lies in the interval (1, 2)

N neha
H Himanshu

As we have learned

Triangle Law of Inequality in Complex Numbers -

$|z_{1}-z_{2}|\geq \left || z_{1} \right |-| z_{2} \right |||$

- wherein

|.| denotes modulus of z in complex numbers

$\left | z+\frac{1}{z} \right |= \left | z-(-\frac{1}{z}) \right |$

$\geq \left | |z|- (-\frac{1}{z}) \right |$

$= |z| - 1/z (\because |z|\geq 2)$

$\geq 2-1/2 = 3/2$

$\left | z+1/z \right |\geq 3/2$

3/2 lies in the interval (1,2)

Option 1)

is strictly greater than

Option 2)

is strictly greater than   but less than

Option 3)

is equal to

Option 4)

lies in the interval (1, 2)

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