Question

find the conjugate of

Answer 1

Hello!

$\blue{\bf{\star \:SOLUTION\: \star}}$

$\dfrac{(3-2i)(2+3i)}{(1+2i)(2-i)}$

⇒ $\dfrac{6+9i-4i-6i^{2}}{2-i+4i-2i^{2}}$

⇒ $\dfrac{6+5i+6}{2+3i+2}$

⇒ $\dfrac{12+5i}{4+3i} \times \dfrac{4-3i}{4-3i}$

⇒ $\dfrac{(12+5i)(4-3i)}{(4)^{2} - (3i)^{2}}$

⇒ $\dfrac{48-36i+20i-15i^{2}}{16+9}$

⇒ $\dfrac{63+16i}{25}$

⇒ $\dfrac{63}{25} + \dfrac{16i}{25}$

Therefore,
$\bf{Conjugate}$ : $\boxed{\dfrac{63}{25} - \dfrac{16i}{25}}$

Cheers!