solve |z + i| = |z - 1| = |1/sqrt[2] + i/sqrt[2] - z|

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. . . . .z+i=z1=12+i2z\displaystyle \left|z\,+\,i\right|\,=\,\left|z\,-\,1\right|\,=\,\left|\frac{1}{\sqrt{2}}\,+\,\frac{i}{\sqrt{2}}\,-\,z\right|
 
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