Question

Find a quadratic equation with roots -1 + 4i and -1- 4i

Answer 1

foil them where
\[ (x-(-1+4i))(x-(-1-4i))\]

Answer 2

\(\bf x=-1 + 4i\implies x+1-4i=0\implies (x+1-4i)=0\\ \quad \\
x=-1- 4i\implies x+1+4i=0\implies (x+1+4i)=0\qquad thus\\ \quad \\
(x+1-4i)(x+1+4i)=0\implies [(x+1)-(4i)][(x+1)+(4i)]=0\\ \quad \\
\textit{recall that }\quad \color{blue}{(a-b)(a+b) = a^2-b^2}\qquad thus\\ \quad \\\
[(x+1)-(4i)][(x+1)+(4i)]=0\\ \quad \\\implies (x+1)^2-(4i)^2\implies (x+1)^2-4^2i^2\\ \quad \\
\textit{recall that }\color{blue}{i^2\implies \sqrt{-1}\cdot \sqrt{-1}\implies \sqrt{(-1)^2}\implies -1}
\)

Answer 3

Thank you so much!

Answer 4

yw