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The range of real number alpha for which...

The range of real number `alpha` for which the equation `z + alpha|z-1| + 2i = 0` has a solution is :

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`Z+alpha|Z-1|+2i=0`
`Z+2i=-alpha|Z-1|`
`alpha=-(Z+2i)/|Z-1|`
`alpha` is real
`|z-1|` is real
`Z=x+iy`
`-iy*2i=0`
`y=-2`
...
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