It is given the complex numbers `z_(1) ` and `z_(2)`, `|z_(1)| =2` and `|z_(2)| =3`. If the included angle of their corresponding vectors is `60^(@)` , then find value of `|(z_(1) +z_(2))/(z_(1) -z_(2))|`

Explanation

Let `z_(1)=2(costheta+isintheta)`
`impliesz_(2)=3((cos(theta+60^(@))+isin(theta+60^(@)))`
`implies(z_(2))/(z_(1))=(3(cos(theta+60^(@))+isin(theta+60^(@))))/(2(costheta+isintheta))`
or`" "(z_(2))/(z_(1))=(3)/(2)(cos60^(@)+isin60^(@))=(3)/(2)((1)/(2)+i(sqrt(3))/(2))`
`:." "|(z_(1)+z_(2))/(z_(1)-z_(2))|=|(1+(z_(2))/(z_(1)))/(1-(z_(2))/(z_(1)))|=|(1+(3)/(2)((1)/(2)+i(sqrt(3))/(2)))/(1-(3)/(2)((1)/(2)+i(sqrt(3))/(2)))|=|(7+i3sqrt(3))/(1-i3sqrt(3))|`
`=(sqrt(49+27))/(sqrt(1+27))=(sqrt(76))/(sqrt(28))=(sqrt(19))/(sqrt(7))`