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

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

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

simplify

\frac{1 + 2 i}{1 - 3 i}

- \frac{1}{2} + \frac{1}{2} i

Solution steps

\frac{1 + 2 i}{1 - 3 i}

Multiply by the conjugate

\frac{1 + 3 i}{1 + 3 i}

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

Simplify

\frac{( 1 + 2 i ) ( 1 + 3 i )}{( 1 - 3 i ) ( 1 + 3 i )} : \frac{- 5 + 5 i}{10}

= \frac{- 5 + 5 i}{10}

Apply the fraction rule:

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

= \frac{- 5}{10} + \frac{5}{10} i

Simplify

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

= - \frac{1}{2} + \frac{1}{2} i

- 5 - - 44

\frac{42}{63}

sec (x) csc (x)

50 b^{4}

\frac{x ^{2} - 4}{x ^{2} + 4} \cdot \frac{x + 2}{x - 2}