Question

Find the following quotient.
(5−4i)/(5+4i)
Answer in the form
(a+bi)/c

.

Answer 1

Answer:

Step-by-step explanation:

$\frac{5-4i}{5+4i}=\frac{(5-4i)*(5-4i)}{(5+4i)*(5-4i)}$

Now numerator is in the form (a - b)² & denominator in the form (a+b)(a - b)

(a -b)² = a² - 2ab + b²

(a + b)(a-b) = a² - b²

$\frac{(5-4i)^{2}}{(5)^{2}-(4i)^{2}}=\frac{5^{2}-2*5*4i+(4i)^{2}}{25-16i^{2}}\\\\=\frac{25-40i+16i^{2}}{25-16*(-1)}\\\\=\frac{25-40i+16*(-1)}{25+16}\\\\=\frac{25-40i-16}{41}\\\\=\frac{9-40i}{41}$