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Question
If \[z_1 = 2 - i, z_2 = - 2 + i,\] find
Im `(1/(z_1overlinez_1))`
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Solution
\[\left( \frac{1}{z_1 z_1} \right) = \frac{1}{\left( 2 - i \right)\left( 2 + i \right)}\]
\[ = \frac{1}{2^2 - i^2}\]
\[ = \frac{1}{5}\]
\[\text { Im }\left( \frac{1}{z_1 z_1} \right) = 0 \left( \text { Since no term containing i is present } \right)\]
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