Question

Find the following quotient.

(5−4i)/(5+4i)
Answer in the form
(a+bi)/c

.

Answer 1

Explanation:

`(5-4i)/(5+4i)=((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

`((5-4i)^(2))/((5)^(2)-(4i)^(2))=(5^(2)-2*5*4i+(4i)^(2))/(25-16i^(2))\\\\=(25-40i+16i^(2))/(25-16*(-1))\\\\=(25-40i+16*(-1))/(25+16)\\\\=(25-40i-16)/(41)\\\\=(9-40i)/(41)`