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Question
Express the following complex number in the standard form a + i b:
\[(1 + i)(1 + 2i)\]
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Solution
\[ \left( 1 + i \right) \left( 1 + 2i \right)\]
\[ = 1 + 2i + i + 2 i^2 \]
\[ = 1 + 3i - 2 \left( \because i^2 = - 1 \right)\]
\[ = - 1 + 3i\]
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