Question

Find the quotient of these complex numbers.(4 + 4i) (5 + 4i) =A.B.C.D.

Answer 1

Find the quotient given below:

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

When managing complex numbers, we must recall:

`\begin{gathered} i^2=-1 \\ \text{ Or, equivalently:} \\ i=√(-1) \end{gathered}`

Multiply and divide the expression by the conjugate of the denominator:

`(4+4i)/(5+4i)\cdot(5-4i)/(5-4i)`

Multiply the expressions in the numerator and in the denominator. We can apply the special product formula in the denominator:

`(a+b)(a-b)=a^2-b^2`

Operating:

`((4+4i)(5-4i))/(5^2-(4i)^2)`

Operate and simplify:

`(20-16i+20i-16i^2)/(25-16i^2)`

Applying the property mentioned above:

`(20-16i+20i+16)/(25+16)`

Simplifying:

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