Question

Find the quotient of these complex numbers. (4+4i)+(5+4i)

Answer 1

`$ (36 + 4i)/(41) $`

Explanation:

We are asked to find the quotient so I am assuming the question should have been:
`$ (4 + 4i)/(5 + 4i) $`.

When we are to find
`$ (a + ib)/(c + id) $` we will multiply the numerator and denominator by the conjugate of the denominator. i.e.,
`$ c - id $`.

Therefore,
`$ (4 + 4i)/(5 + 4i) * (5 - 4i)/(5 - 4i) $`

`$ ((4 + 4i)(5 - 5i))/(25 + 16)  \hspace{20mm}  [ Since, (a + ib)(a - ib) = a^2 + b^2] $`.

Multiplying the numerator, we have:
`$ 20 - 16i + 20i + 16 $`.

Therefore the answer is:
`$ (36 + 4i)/(25 + 16) = (36 + 4i)/(41) $`.

Hence, the answer.