if arg (z^1/3) =1/2 arg( z^2 +zbar * z^1/3 ) then find value of |z|

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Please find below the solution to the asked query:

We haveargz13=argz2+z¯+z132argz2+z¯.z13=2argz13argz2+z¯.z13=argz23argz2+z¯.z13-argz23=0argz2+z¯.z13z23=0argz2z23+z¯.z13z23=0argz43+z¯z-13=0argz43+zz¯z-13z=0argz43+z2.z-43=0 As zz¯=z2Which means that z43+z2.z-43 lies on real axis. It should be evidentthat this requires z=1

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