Answer
$\dfrac{6+2i}{4-3i}=\dfrac{18}{25}+\dfrac{26}{25}i$
Work Step by Step
$\dfrac{6+2i}{4-3i}$
Multiply the numerator and the denominator of this expression by the complex conjugate of the denominator:
$\dfrac{6+2i}{4-3i}=\dfrac{6+2i}{4-3i}\cdot\dfrac{4+3i}{4+3i}=\dfrac{(6+2i)(4+3i)}{4^{2}-(3i)^{2}}=...$
$...=\dfrac{24+18i+8i+6i^{2}}{16-9i^{2}}=...$
Substitute $i^{2}$ by $-1$ and simplify:
$...=\dfrac{24+18i+8i+6(-1)}{16-9(-1)}=\dfrac{24+26i-6}{16+9}=\dfrac{18+26i}{25}=...$
$...=\dfrac{18}{25}+\dfrac{26}{25}i$
