Answer:
[tex]$ \frac{36 + 4i}{41} $[/tex]
Step-by-step explanation:
We are asked to find the quotient so I am assuming the question should have been: [tex]$ \frac{4 + 4i}{5 + 4i} $[/tex].
When we are to find [tex]$ \frac{a + ib}{c + id} $[/tex] we will multiply the numerator and denominator by the conjugate of the denominator. i.e., [tex]$ c - id $[/tex].
Therefore, [tex]$ \frac{4 + 4i}{5 + 4i} \times \frac{5 - 4i}{5 - 4i} $[/tex]
[tex]$ \frac{(4 + 4i)(5 - 5i)}{25 + 16} \hspace{20mm} [ Since, (a + ib)(a - ib) = a^2 + b^2] $[/tex].
Multiplying the numerator, we have: [tex]$ 20 - 16i + 20i + 16 $[/tex].
Therefore the answer is: [tex]$ \frac{36 + 4i}{25 + 16} = \frac{36 + 4i}{41} $[/tex].
Hence, the answer.
