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Determinate-the-geometric-aspect-described-by-M-z-in-complex-plane-such-that-arg-z-3-i-pi-4-2pi-




Question Number 122659 by mathocean1 last updated on 18/Nov/20
Determinate the geometric  aspect described by M(z) in  complex plane such that:  arg(z^− −3+i)≡(π/4)[2π]
DeterminatethegeometricaspectdescribedbyM(z)incomplexplanesuchthat:arg(z3+i)π4[2π]
Answered by MJS_new last updated on 18/Nov/20
arg (x) ≡(π/4)[2π] ⇔ x=c+ci  let z=a+bi ⇒ z^− =a−bi  a−bi−3+i=c+ci  ⇒  { ((a−c−3=0 ⇒ c=a−3)),((−b−c+1=0 ⇒ c=1−b)) :}  a−3=1−b ⇒ b=4−a  z=a+(4−a)i  this is a straight line.
arg(x)π4[2π]x=c+ciletz=a+biz=abiabi3+i=c+ci{ac3=0c=a3bc+1=0c=1ba3=1bb=4az=a+(4a)ithisisastraightline.

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