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Please solve above 2 problems with deatailed solution kindly .thankyou

Please solve above 2 problems with deatailed solution kindly .thankyou

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Grade:12th pass

1 Answers

Aditya Gupta
2081 Points
5 years ago
1. ​we know that trianagle inequality states that
    |z1+z2+z3| less than equal to |z1|+ |z2|+ |z3|
    now,  |z1-1+1| less than equal to |z1-1|+|1| = 2
    similarly |z2-2+2| less than equal to |z2-2|+|2| = 4 
   and |z3-3+3| less than equal to |z3-3|+|3| = 6
   adding all these inequalities, we obtain  |z1+z2+z3| less than equal to 2+4+6=12
   hence the greatest value of  |z1+z2+z3| is 12, which occurs when z1=2, z2=4 and z3=6
2. we can write z= (1+cos2pi/5) – isin(2pi/5)
    so let argz= x
    then tanx= – sin(2pi/5)/(1+cos2pi/5) = – tanpi/5
    so, argz = – pi/5

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