# 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) $\frac{5+2i}{9}$

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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