\([ (\frac{1}{5}+\frac{7i}{5})-(6+\frac{i}{5})]-\rm (\frac{-4}{5}+i)\) का मान ज्ञात कीजिए।

  1. \(\rm (-5+\frac{i}{5})\)
  2. \(\rm (-5-i)\)
  3. -i
  4. 0

Answer (Detailed Solution Below)

Option 1 : \(\rm (-5+\frac{i}{5})\)
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Detailed Solution

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गणना:

\([ (\frac{1}{5}+\frac{7i}{5})-(6+\frac{i}{5})]-\rm (\frac{-4}{5}+i)\)

\(\rm (\frac{1}{5}-6+\frac{7i}{5}-\frac{i}{5})-\rm (\frac{-4}{5}+i)\)

=  \(\rm (\frac{-29}{5}+\frac{6i}{5})-\rm (\frac{-4}{5}+i)\)

\(\rm (\frac{-29}{5}+\frac{4}{5}+\frac{6i}{5}-i)\)

\(\rm (\frac{-25}{5}+\frac{i}{5})\)

\(\rm (-5+\frac{i}{5})\)

इसलिए, विकल्प (1) सही है।
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