What is (2-i)/(3-i)-1/5 ((1+8i)/(1+3i)) ?

The solution to (2-i)/(3-i)-1/5 ((1+8i)/(1+3i)) is 1/5-1/5 i

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simplify (2-i)/(3-i)-1/5 ((1+8i)/(1+3i))

simplify

\frac{2 - i}{3 - i} - \frac{1}{5} (\frac{1 + 8 i}{1 + 3 i})

\frac{1}{5} - \frac{1}{5} i

Solution steps

\frac{2 - i}{3 - i} - \frac{1}{5} (\frac{1 + 8 i}{1 + 3 i})

\frac{2 - i}{3 - i} = \frac{7 - i}{10}

\frac{1 + 8 i}{1 + 3 i} = \frac{25 + 5 i}{10}

= \frac{7 - i}{10} - \frac{1}{5} \cdot \frac{25 + 5 i}{10}

Simplify

\frac{1}{5} \cdot \frac{25 + 5 i}{10} : \frac{\frac{5}{2} + \frac{1}{2} i}{5}

= \frac{7 - i}{10} - \frac{\frac{5}{2} + \frac{1}{2} i}{5}

Join

\frac{7 - i}{10} - \frac{\frac{5}{2} + \frac{1}{2} i}{5} : \frac{- i + 1}{5}

= \frac{- i + 1}{5}

Rewrite in standard complex form:

\frac{1}{5} - \frac{1}{5} i

= \frac{1}{5} - \frac{1}{5} i

(\frac{9 + 5 i}{3 - 2 i})^{2}

72 + 32 + 18

m^{2} - 10 m + 9

\frac{a}{3} = \frac{a - 3}{2}

lo g_{2} (\frac{1}{16}) = x

What is (2-i)/(3-i)-1/5 ((1+8i)/(1+3i)) ?
The solution to (2-i)/(3-i)-1/5 ((1+8i)/(1+3i)) is 1/5-1/5 i