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Ask iit jee aieee pet cbse icse state board experts Expert Question: the max. value of |z| where z satisfiies the condition |z+2/z|=2 is
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bhargava (0)

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the max. value of |z| where z satisfiies the condition |z+2/z|=2 is
    

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feynmann (2472)

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take z= r exp ( i@)


Now put this value in the given qty and then u will find a quadratic eqn in r . ( with @ as a parameter)


Solve for r and see for what value of @ r gets max .

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pramod6990 (1025)

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u cud do it usng dis way also.....put z= R (cos@ + i sin@)


u have the reqd. expression as / R (cos @ + isin@ ) + (1/R)(cos @ - isin@ ) / = 2 ...u cud dus proceed and solve for max value of R....


rate if useful...


"Logic is the systematic way of reaching the wrong conclusion with confidence" lol.....
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hsbhatt (6235)

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|z| - \frac{2}{|z|} \le \left|z+\frac{2}{|z|} \right | = 2 \\ \\<br/>\Rightarrow |z|^2 - 2|z| - 2 \le 0 \\ \\<br/>\Rightarrow (|z| -1)^2 \le 3 \\ \\<br/>\Rightarrow |z| \le \sqrt 3 +1


Time wounds all heels
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