What is (1-5i)/(3-i)+i^{46} ?

The solution to (1-5i)/(3-i)+i^{46} is -1/5-7/5 i

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simplify (1-5i)/(3-i)+i^{46}

simplify

\frac{1 - 5 i}{3 - i} + i^{46}

- \frac{1}{5} - \frac{7}{5} i

Solution steps

\frac{1 - 5 i}{3 - i} + i^{46}

\frac{1 - 5 i}{3 - i} = \frac{8 - 14 i}{10}

i^{46} = - 1

= \frac{8 - 14 i}{10} - 1

Join

\frac{8 - 14 i}{10} - 1 : \frac{- 1 - 7 i}{5}

= \frac{- 1 - 7 i}{5}

Apply the fraction rule:

\frac{a + bi}{c} = \frac{a}{c} + \frac{b}{c} i

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

Simplify

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

= - \frac{1}{5} - \frac{7}{5} i

9 \frac{3}{8} - 4.37

\frac{4}{5} - 4

\frac{1}{2} \div \frac{5}{7}

- 18 \cdot - 10

2 x^{3} - 3 x^{2} - 9 x + 10