If `2z_1//3z_2`is a purely imaginary number, then find the value of `"

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