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Please solve above 2 problems with deatailed solution kindly .thankyou

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Manoj

7 Years agoGrade 12th pass

1 Answer

Aditya Gupta

7 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

Please send the full solution as soon as possible 🙏

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