conjugate of frac{(3-2 i)(2+3 i)}{(1+2 i)(2-i)} .

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4-1.Complex numbers

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Find the conjugate of $\frac{(3-2 i)(2+3 i)}{(1+2 i)(2-i)}$.

A

$\frac{63}{25}+\frac{16}{25} i$

B

$\frac{63}{25}+\frac{16}{25} i$

C

$\frac{63}{25}+\frac{16}{25} i$

D

$\frac{63}{25}+\frac{16}{25} i$

Solution

We have, $\frac{(3-2 i)(2+3 i)}{(1+2 i)(2-i)}$

$=\frac{6+9 i-4 i+6}{2-i+4 i+2}=\frac{12+5 i}{4+3 i} \times \frac{4-3 i}{4-3 i} $

$=\frac{48-36 i+20 i+15}{16+9}=\frac{63-16 i}{25}=\frac{63}{25}-\frac{16}{25} i$

Therefore, conjugate of $\frac{(3-2 i)(2+3 i)}{(1+2 i)(2-i)}$ is $\frac{63}{25}+\frac{16}{25} i$.

Standard 11

Mathematics

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