Answer:
Step-by-step explanation:
(1 - i) / (sqrt(3 + 4i)
= (1 - i) / [tex]\sqrt{3 + 4i}[/tex]
=> multiply and divide by conjugate of denominator
= [tex](1 - i) / \sqrt{3 + 4i} * \sqrt{3 - 4i} / \sqrt{4 - 3i}[/tex]
= [tex](1 - i)*(\sqrt{3 - 4i} ) / (\sqrt{3 + 4i} *\sqrt{3 - 4i})[/tex]
= [tex](1 - i) * (\sqrt{3 - 4i} ) / \sqrt{(9 - 16i^{2} )[/tex]
= [tex](1 - i) * (\sqrt{3 - 4i} ) / \sqrt{(9 - (-16) )[/tex]
= [tex](1 - i) * \sqrt{3 - 4i} ) / \sqrt{25}[/tex]
= [tex](1 - i) * \sqrt{3 - 4i} / 5[/tex]
= [tex]\sqrt{(1 - i)^{2} } * \sqrt{3 - 4i} / 5[/tex]
= [tex]\sqrt{(1 + -1 -2i)*(3 - 4i)} / 5 \\\sqrt{-2i * (3 - 4i)} / 5\\\sqrt{-6i + 8*-1} /5 \\\sqrt{-6i - 8 } / 5[/tex]
