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