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Question
Express the following complex number in the standard form a + i b:
\[\frac{3 + 2i}{- 2 + i}\]
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Solution
\[\frac{3 + 2i}{- 2 + i}\]
\[ = \frac{3 + 2i}{- 2 + i} \times \frac{- 2 - i}{- 2 - i}\]
\[ = \frac{- 6 - 3i - 4i - 2 i^2}{4 - i^2} \left( \because i^2 = - 1 \right)\]
\[ = \frac{- 6 - 7i + 2}{4 + 1}\]
\[ = \frac{- 4 - 7i}{5}\]
\[ = \frac{- 4}{5} - \frac{7}{5}i\]
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