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Home » x \equiv -1 \pmod9 \quad \textand \quad x \equiv 1 \pmod7 - Silent Sales Machine

x \equiv -1 \pmod9 \quad \textand \quad x \equiv 1 \pmod7 - Silent Sales Machine

📅 March 10, 2026 👤 scraface

Mar 10, 2026

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Try \( a = -b \):
Let \( b = -a \), then (2): \( 2a(-a) = -2a^2 = -2 \Rightarrow a^2 = 1...
If \( a = 1 \), \( b = -1 \), then \( (a + bi)^2 = (1 - i)^2 = 1 - 2i...
If \( a = -1 \), \( b = 1 \), \( (-1 + i)^2 = 1 - 2i + i^2 = -2i \) ✅
So the square roots are \( 1 - i \) and \( -1 + i \)
Now,
\[ z = \frac{-(1 + i) \pm (1 - i)}{2} \]
First solution:
\[ z = \frac{-1 - i + 1 - i}{2} = \frac{-2i}{2} = -i \]
Second solution:

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