Question

Express 4xi + 5yi^8 + 6xi^3 + 2yi^4 in simplest a+bi form

Answer 1

\[4x \iota+5y \iota^8+6x \iota^3+2y \iota^4\]
\[=4x \iota+5y \left( \iota^2 \right)^4+6x \left( \iota^2 \right)\iota+2 y \left( \iota^2 \right)^2\]
\[\iota^2=-1\]
simplify it.

Answer 2

\(\large \begin{array}{llll}
4xi\implies 4x\cdot i
\\ \quad \\
5yi^8\implies 5y\cdot i^2\cdot i^2\cdot i^2\cdot i^2
\\ \quad \\
6xi^3\implies 6x\cdot i^2\cdot i
\\ \quad \\
2yi^4 \implies 2y\cdot i^2\cdot i^2
\end{array}
\\ \quad \\
\bf {\color{blue}{ recall\implies i^2\implies \sqrt{-1}\cdot \sqrt{-1}\implies \sqrt{(-1)^2}\implies -1}}\)

what do you think?