Answer:
B.
Step-by-step explanation:
[tex] \frac{4 + 4i}{5 + 4i} [/tex]
- Multiplying both numerator and denominator by (5 - 4i) , the conjugate of the denominator, i. e, (5 + 4i).
[tex] \frac{4 + 4i}{5 + 4i} \times \frac{5 - 4i}{5-4i} [/tex]
[tex] \frac{(4 + 4i)(5 - 4i)}{(5 + 4i)(5 - 4i)} [/tex]
- Multiplying (4+4i) and (5-4i) using distributive property
- Using the identity (a+b)(a-b)= a² - b² where 5 will act as a and 4i will act as b
[tex] \frac{20-16i+20i-16i^2}{(5) {}^{2} - (4i) {}^{2} } [/tex]
(combining like terms)
[tex] \frac{20+(-16i+20i)-(-16)}{25-(-16)} [/tex]
[tex] \frac{(20+16)+4i}{25+16} [/tex]
[tex] \frac{36+4i}{41} [/tex]
distributing the denominator
[tex] \frac{36}{41} + \frac{4}{41}i [/tex]
That is, option B.
