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If 2z1//3z2 is a purely imaginary number...

If `2z_1//3z_2` is a purely imaginary number, then find the value of `"|"(z_1-z_2")"//(z_1+z_2)|dot`

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As given, let
`(2z_(1))/(3z_(2))=iy" or "(z_(1))/(z_(2))=(3)/(2)iy`
so that `|(z_(1)-z_(2))/(z_(1)+z_(2))|=|((z_(1))/(z_(2))-1)/((z_(1))/(z_(2))+1)|=|((3)/(2)iy-1)/((3)/(2)iy+1)|=|(1-(3)/(2)iy)/(1+(3)/(2)iy)|=1`
`" "[because|z|=|bar(z)|]`
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