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Mice21 [21]
3 years ago
12

3-2i/1+4i include each step necessary in simplifying

Mathematics
1 answer:
Likurg_2 [28]3 years ago
8 0

Answer:

\frac{3-2i}{1+4i}=\frac{11}{17}-\frac{10}{17}i

Step-by-step explanation:

\frac{3-2i}{1+4i} <-- Given

\frac{3-2i}{1+4i}*\frac{1-4i}{1-4i} <-- Multiply by the conjugate of the denominator as a factor of 1

\frac{(3-2i)(1-4i)}{(1+4i)(1-4i)}

\frac{(3)(1)+3(-4i)-2i(1)-2i(4i)}{(1)(1)+1(-4i)+4i(1)+4i(-4i)} <-- Use the Distributive Property and FOIL

\frac{3-12i-2i-8i^2}{1-4i+4i-16i^2}

\frac{3-10i-8i^2}{1-16i^2}

\frac{3-10i-8(-1)}{1-16(-1)} <-- Rewrite i^2 as -1

\frac{3-10i+8}{1+16}

\frac{11-10i}{17}

\frac{11}{17}-\frac{10}{17}i <-- Rewrite in a\pm bi form

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