Question

Divide the following complex numbers:xFormula1" title="(2 + i) \div (1 - 4i)" alt="(2 + i) \div (1 - 4i)" align="absmiddle" class="latex-formula">
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Answer 1

Answer:

$-\dfrac{2}{17} + \dfrac{9}{17}i$

Step-by-step explanation:

$(2 + i) \div (1 - 4i) =$

$= \dfrac{2 + i}{1 - 4i}$

$= \dfrac{2 + i}{1 - 4i} \times \dfrac{1 + 4i}{1 + 4i}$

$= \dfrac{(2 + i)(1 + 4i)}{(1 - 4i)(1 + 4i)}$

$= \dfrac{2 + 8i + i + 4i^2}{1 + 16}$

$= \dfrac{2 + 9i - 4}{17}$

$= \dfrac{-2 + 9i}{17}$

$= -\dfrac{2}{17} + \dfrac{9}{17}i$