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Express the Following Complex Number in the Standard Form a + I B: 3 + 2 I − 2 + I - Mathematics

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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APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 13 Complex Numbers
Exercise 13.2 | Q 1.02 | Page 31
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