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if z=1/2 (i√3-1) , then find the value of (z -z2 +2z3) x (2-z+z2) is ?

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1 Answer

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Given z=1/2 (i√3-1)

=>z2=1/4 (i√3-1)2

        =1/4(-3-2√3i+1)

        = -1/4×2(√3i+1)

       = -1/2(√3i+1)

So    z3=z2×z=-1/2(√3i+1)x1/2 (√3i-1)= -1/4(-3-1)=1

Now

(z -z2 +2z3) x (2-z+z2)

=(z -z2 +2.1) x (2-z+z2)

=(2 -z2 +z) x (2-z+z2)

={2 -(z2-z)} {2 +(z2-z)}

=4-(z4-2z3+z2)

=4-(z-2+z2)

=4-(1/2 (i√3-1)-2-1/2(√3i+1)

=4-(-1/2 -2-1/2)

=4-(-1-2)=4+3=7

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