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Help me solve this - Algebra - BITSAT

If z \times (3+4i)=2+3i, then the value of z is:

  • Option 1)

    \frac{18-i}{25}

  • Option 2)

    \frac{9+9i}{16}

  • Option 3)

    \frac{18+i}{25}

  • Option 4)

    \frac{5+2i}{9}

 
Answers (1)
101 Views
P Plabita

As we learnt in 

Division of Complex Numbers -

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

-

 

 \\Z\times \left ( 3+4i \right )=2+3i\\*\\*Z=\frac{2+3i}{3+4i}=\frac{\left (2+3i \right )\left ( 3-4i \right )}{\left (3+4i \right )\left ( 3-4i \right )}\\*\\*= > \frac{6+9i-8i+12}{25}= > \frac{18+i}{25}


Option 1)

\frac{18-i}{25}

Incorrect

Option 2)

\frac{9+9i}{16}

Incorrect

Option 3)

\frac{18+i}{25}

Correct

Option 4)

\frac{5+2i}{9}

Incorrect

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