If z1=2-i ,\ z2=1+i , find |(z1+z2+1)/(z...

If `z_1=2-i ,\ z_2=1+i ,` find `|(z_1+z_2+1)/(z_1-z_2+i)|`.

Text Solution

Verified by Experts

Given `z_1=2-i ,\ z_2=1+i ,`
And we have to find
`|(z_1+z_2+1)/(z_1-z_2+i)|`
So on putting values in this we get,
`|(z_1+z_2+1)/(z_1-z_2+i)|=|((2-i)+(1+i)+1)/((2-i)-(1+i)+i)|`
`|(z_1+z_2+1)/(z_1-z_2+i)|=|(2-i+1+i+1)/(2-i-1-i+i)|`
`|(z_1+z_2+1)/(z_1-z_2+i)|=|4/(1-i)|`
Now multiply and divide this by (1+i) we get,
...

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if z_(1)=3+i and z_(2) = 2-i, " then" |(z_(1) +z_(2)-1)/(z_(1) -z_(2)+i)| is

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