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Q. If (z+1)^7 +(z)^7=0 have roots z1,z2,.....,z7,where z is a complex number.find the value of summation of i=1 to r=7 Re(Zr)




  • Q. If (z+1)^7 +(z)^7=0 have roots z1,z2,.....,z7,where z is a complex number.find the value of summation of i=1 to r=7 Re(Zr)




Grade:upto college level

1 Answers

Radhika Batra
247 Points
7 years ago
open (1+z)^7 = 1+7z...........+7z^6 +z^7 -----binomial theorom

putting in the given equation we get

2 z^7 + 7 z^6 .............. +1 = 0

as z1 , z2 ......z7 are the roots of above equation

z1+z2+........z7 = -7/2  ...........theory of equations; sum of roots = - (coeff. of second last  term/coeff of the highest term)

z1 = re(z1) + i img (z1)  similarly others

now comparing real part of L.H.S and R.H.S

we get summation of real part of z1 to z7 = -7/2

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