If `(5z_1)/(7z_2)` is purely imaginary then `|(2z_1+3z_2)/(2z_1-3z_2)| – InterviewSolution

InterviewSolution

1.	If `(5z_1)/(7z_2)` is purely imaginary then `\|(2z_1+3z_2)/(2z_1-3z_2)\|=`
Answer» `z_1=r_1e^(itheta_1)` `z_2=r_1e^(itheta_2)` `5z_1/7z_2->(5r_1e^(itheta_1))/(7r_2e^(itheta_2)` `theta_1-theta_2=2npipmpi/2` `\|(2z_1+3z_2)/(2z_1-3z_2)\|` `\|(1+3/2z_2/z_1)/(1-3/2z_2/z_1)\|` `\|(1+3/2x i)/(1-3/2x i)\|` `sqrt(1^2+(3/2x)^2)/sqrt(1^2+(-3/2x)^2)` `1`

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