Question

(4 + 4i)/(5+4i) = divide

Answer 1

Answer:

B.

Step-by-step explanation:

$\frac{4 + 4i}{5 + 4i}$

• Multiplying both numerator and denominator by (5 - 4i) , the conjugate of the denominator, i. e, (5 + 4i).

$\frac{4 + 4i}{5 + 4i} \times \frac{5 - 4i}{5-4i}$

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

• 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

$\frac{20-16i+20i-16i^2}{(5) {}^{2} - (4i) {}^{2} }$

• i² = -1

(combining like terms)

$\frac{20+(-16i+20i)-(-16)}{25-(-16)}$

$\frac{(20+16)+4i}{25+16}$

$\frac{36+4i}{41}$

distributing the denominator

$\frac{36}{41} + \frac{4}{41}i$

That is, option B.