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  • Help me please, - Complex numbers and quadratic equations - JEE Main-9

\frac{2+3i}{1+i}  equals

  • Option 1)

    \frac{5}{2}-\frac{i}{2}

  • Option 2)

    \frac{-5}{2}-\frac{i}{2}

  • Option 3)

    \frac{5}{2}+\frac{i}{2}

  • Option 4)

    \frac{-5}{2}+\frac{i}{2}

 

Answers (1)

best_answer

\because \frac{a+ib}{c+id}=\frac{ac+bd}{c^{2}+d^{2}}+i\left ( \frac{bc-ad}{c^{2}+d^{2}} \right )

in above equation a=2, b-3, c=1, d=1

\therefore \: \frac{2+3i}{1+i}=\frac{2+3}{1+1}+i\frac{\left ( 3-2 \right )}{1+1}=\frac{5}{2}+\frac{1}{2}i

\therefore Option (C)

 

Division of Complex Numbers -

\frac{a+ib}{c+id}=\frac{ac+bd}{c^{2}+d^{2}}+i\frac{bc-ad}{c^{2}+d^{2}}

-

 

 


Option 1)

\frac{5}{2}-\frac{i}{2}

This is incorrect

Option 2)

\frac{-5}{2}-\frac{i}{2}

This is incorrect

Option 3)

\frac{5}{2}+\frac{i}{2}

This is correct

Option 4)

\frac{-5}{2}+\frac{i}{2}

This is incorrect

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