Question

Perform the indicated operation & simplify. Express the answer in terms of i (as a complex number).(2+4i)⋅(2+4i) =

Answer 1

You have the following expression;

$(2+4i)(2+4i)$

to perform the previous operation, expand the previous factors as follow:

$\begin{gathered} (2+4i)(2+4i)=(2)(2)+(2)(4i)+(4i)(2)+(4i)(4i) \\ =4+8i+8i+16i^2 \\ =4+16i+16i^2 \end{gathered}$

take into account that i^2 = -1, then, you obtain:

$4+16i+16(-1)=4+16i-16=16i-12$

Hence, the result is 16i - 12