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If |z(1)|=|z(2)|=....|z(n)|=1, then show...

If `|z_(1)|=|z_(2)|=....|z_(n)|=1`, then show that, `|z_(1)+z_(2)+z_(3)+....z_(n)|= |(1)/(z_(1))+(1)/(z_(2))+(1)/(z_(3))+...+(1)/(z_(n))|`

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The correct Answer is:
`|(1)/(z_(1))+(1)/(z_(2))+...+(1)/(zn)|`
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KUMAR PRAKASHAN-COMPLEX NUMBERS AND QUADRATIC EQUATIONS-SOLUTIONS OF NCERT EXEMPLAR PROBLEMS (LONG ANSWER TYPE QUESTIONS)
  1. If |z(1)|=1(z(1) ne -1) and z(2)=(z(1)-1)/(z(1)+1) then show that the ...

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  2. If z(1), z(2) and z(3), z(4) are two pairs of conjugate complex number...

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  3. If |z(1)|=|z(2)|=....|z(n)|=1, then show that, |z(1)+z(2)+z(3)+....z(n...

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  4. If the complex numbers z(1) and z(2) arg (z(1))- arg(z(2))=0 then show...

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  5. Solve the system of equation Re(z^(2))=0,|z|=2.

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  6. Find the complex number satsifying the equation z+sqrt(2)|(z+1)|+i=0

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  7. Convert the complex number z=(1-i)/(cos pi/3 + I sin pi/3) in the pola...

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  8. If z and we are two complex numbers such that |zw|=1 and arg(z)-arg(w)...

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  9. Fill in the blanks of the following For any two complex numbers z(1)...

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  10. Fill in the blanks of the following the value of sqrt(-25)xxsqrt(-9)...

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  11. Fill in the blanks of the following The number ((1-i)^(2))/(1-i^(3))...

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  12. Fill in the blanks of the following The sum of the series i+i^(2)+i^...

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  13. Fill in the blanks of the following Multiplicative inverser of 1+I i...

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  14. Fill in the blanks of the following If z(1) and z(2) are complex num...

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  15. Fill in the blanks of the following arg(z)+ arg(barz) where (barz ne...

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  16. Fill in the blanks of the following If |z+4| le3, then the greatest ...

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  17. Fill in the blanks of the following If |(z-2)/(z+2)|=(pi)/(6) then t...

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  18. Fill in the blanks of the following If |z|=4" and arg"(z)=(5pi)/(6),...

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  19. State true of false for the following: The order relation is defined...

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  20. State true of false for the following: Multiplication of a non-zero ...

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