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  • How to solve this problem- - Complex numbers and quadratic equations - JEE Main-3

If z= \frac{6-3i}{2+i}  then Re\left ( z \right )-Im\left ( z \right )  equals  

  • Option 1)

    \frac{21}{5}

  • Option 2)

    \frac{22}{5}

  • Option 3)

    \frac{23}{5}

  • Option 4)

    \frac{24}{5}

 

Answers (1)

best_answer

z=\frac{6-3i}{2+i}=\frac{\left ( 6\times 2 \right )+\left ( -3 \right )\times 1}{4+1}+\frac{i\left ( \left ( -3 \right )\left ( 2 \right )-\left ( 6 \right )\left ( 1 \right ) \right )}{4+1}

\Rightarrow \: z=\frac{9}{5}+i\left ( \frac{-12}{5} \right )

\therefore Re\left ( z \right )=\frac{9}{5}  and  \therefore Im\left ( z \right )=\frac{-12}{5}

Re\left ( z \right )-Im\left ( z \right )=\frac{9}{5}-\left ( \frac{-12}{5} \right )=\frac{21}{5}

\therefore Option (A)

 

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{21}{5}

This is correct

Option 2)

\frac{22}{5}

This is incorrect

Option 3)

\frac{23}{5}

This is incorrect

Option 4)

\frac{24}{5}

This is incorrect

Posted by

Himanshu

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