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if z^4= (z-1)^4 then the roots of the equation are represented in the argand plane are by points that are: a)collinear b)concyclic c)vertices of parallelogram d)none

if z^4= (z-1)^4 then the roots of the equation are represented in the argand plane are by points that are:
a)collinear
b)concyclic
c)vertices of parallelogram
d)none

Grade:Upto college level

1 Answers

Chetan Mandayam Nayakar
312 Points
10 years ago

Dear Mukul,

z^4=(z-1)^4

z^2=±(z-1)^2

a)let z^2=+(z-1)^2, 2z=1,z=1/2

b)let z^2=-(z-1)^4

2z2-2z+1=0

z=(1/2)±(i/2)

So the solution set consists of 1/2,1/2 +i/2, 1/2 -i/2, which are obviously collinear

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