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If alpha = (z - i)//(z + i) show that, ...

If `alpha = (z - i)//(z + i)` show that, when z lies above the real axis, `alpha`will lie within the unit circle which has centre at the origin. Find the locus of `alpha ` as z travels on the real axis form `-oo "to" + oo`

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To solve the problem, we need to show that when \( z \) lies above the real axis, \( \alpha \) will lie within the unit circle centered at the origin. We also need to find the locus of \( \alpha \) as \( z \) travels along the real axis from \( -\infty \) to \( +\infty \). ### Step-by-Step Solution: 1. **Define \( z \)**: Let \( z = x + iy \), where \( y > 0 \) (since \( z \) lies above the real axis). 2. **Substitute \( z \) into \( \alpha \)**: ...
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