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Question
If z1 = 2 – i, z2 = 1 + i, find `|(z_1 + z_2 + 1)/(z_1 - z_2 + 1)|`
Solution
`z_1 = 2 - i, z_2 = 1 + i`
∴ `|(z_1 + z_2 + 1)/(z_1 - z_2 + 1)| = |((2-i)+(1 + i)+1)/((2-i) - (1 + i) + 1)|`
= `|4/(2-2i)| = |4/(2(1 - i))|`
= `|2/(1 - i) xx (1 + i)/(1 + i)| = |(2(1 + i))/(1^2 - i^2)|`
= `|(2(1 + i))/(1 + 1)|` [i2 = - 1]
= `|(2(1 +i))/2|`
= `1 + i = sqrt(1^2 + 1^2) = sqrt2`
The value of this type is `|(z_1 + z_2 + 1)/(z_1 - z_2 + 1)| "is" sqrt2`
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