Question

Find the quotient of these complex numbers (4-6i)/(2-5i)

Answer 1

Answer:

$\frac{38}{29} + \frac{8}{29}i$

Step-by-step explanation:

We have to find the quotient of the division of complex numbers $\frac{(4 - 6i)}{(2 - 5i)}$.

Now, we have to get the expression in simplified form.

$\frac{(4 - 6i)}{(2 - 5i)}$

= $\frac{(4 - 6i)(2 + 5i)}{(2 - 5i)(2 + 5i)}$ {Rationalizing the denominator}

= $\frac{4(2 + 5i) - 6i(2 + 5i)}{2^{2} - (5i)^{2}}$

= $\frac{8 + 20i - 12i - 30(i)^{2}}{4 + 25}$

{Since, i = √(- 1) i.e. square root of negative one, hence, i² = - 1}

= $\frac{8 + 30 + 8i}{29}$

= $\frac{38}{29} + \frac{8}{29}i$ (Answer)