How to solve the simultaneous equations ∣z + 1∣ = ∣z − 1∣, ∣z + 2∣ = ∣z − 3∣?

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Answer 1 · 2018-04-16T12:56:26

No solution

#abs z = sqrt(z bar z)# then

#abs(z+1) = sqrt((z+1)(bar z +1)) = abs(z-1) = sqrt((z-1)(bar z-1)) #

and

#abs(z+2) = sqrt((z+2)(bar z +2)) = abs(bar z-3) = sqrt((bar z-3)(z-3)) #

or

#{(bar z z + z+bar z + 1 = bar z z -(barz + z) + 1),(z bar z + 2(z+bar z)+4=barz z -3(barz + z)+ 9):}#

or

#{(z+bar z = -(barz + z)),(2(z+bar z)=-3(barz + z)+ 5):}#

or

#{(z+bar z = 0),(z+bar z = 1):}#

so no solution is possible.