Question

The quotient of 5i and 2 − i

Answer 1

`\bf \cfrac{5i}{2-i}\cdot \cfrac{2+i}{2+i}\impliedby \textit{multiplying by the conjugate of the bottom}\\\\ -------------------------------\\\\ \textit{also recall }\textit{difference of squares} \\ \quad \\ (a-b)(a+b) = a^2-b^2\qquad \qquad a^2-b^2 = (a-b)(a+b) \\\\\\ \textit{and also that }i^2=-1\\\\ -------------------------------\\\\`


`\bf \cfrac{5i(2+i)}{(2-i)(2+i)}\implies \cfrac{5i(2+i)}{2^2-i^2}\implies \cfrac{5i(2+i)}{4-(-1)}\implies \cfrac{5i(2+i)}{5} \\\\\\ i(2+i)\implies 2i+i^2\implies 2i+(-1)\implies 2i-1\implies -1+2i`

Answer 2

-1 + 2i

hope this helps! :o)