Algebra of complex numbers

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Question

The number of complex numbers z such that $(1 + i) z = i |z|$

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Solution

$\begin{array}{l} | (1 + i) z | = | i | z ∥ \\ \Rightarrow \sqrt{2} | z | = | z | \Rightarrow (\sqrt{2} - 1) | z | = 0 \\ \Rightarrow | z | = 0 \Rightarrow z = 0 \end{array}$

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