Answer:
[tex]\frac{38}{29} + \frac{8}{29}i[/tex]
Step-by-step explanation:
We have to find the quotient of the division of complex numbers [tex]\frac{(4 - 6i)}{(2 - 5i)}[/tex].
Now, we have to get the expression in simplified form.
[tex]\frac{(4 - 6i)}{(2 - 5i)}[/tex]
= [tex]\frac{(4 - 6i)(2 + 5i)}{(2 - 5i)(2 + 5i)}[/tex] {Rationalizing the denominator}
= [tex]\frac{4(2 + 5i) - 6i(2 + 5i)}{2^{2} - (5i)^{2}}[/tex]
= [tex]\frac{8 + 20i - 12i - 30(i)^{2}}{4 + 25}[/tex]
{Since, i = √(- 1) i.e. square root of negative one, hence, i² = - 1}
= [tex]\frac{8 + 30 + 8i}{29}[/tex]
= [tex]\frac{38}{29} + \frac{8}{29}i[/tex] (Answer)
