- Home
- Standard 11
- Mathematics
4-1.Complex numbers
medium
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
