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

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

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

simplify

\frac{- 1 + 5 i}{2 + 3 i}

1 + i

Solution steps

\frac{- 1 + 5 i}{2 + 3 i}

Multiply by the conjugate

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

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

Simplify

\frac{( - 1 + 5 i ) ( 2 - 3 i )}{( 2 + 3 i ) ( 2 - 3 i )} : \frac{13 + 13 i}{13}

= \frac{13 + 13 i}{13}

Apply the fraction rule:

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

= \frac{13}{13} + \frac{13}{13} i

Simplify

\frac{13}{13} + \frac{13}{13} i : 1 + i

= 1 + i

\frac{39}{10}

20 - (- 5)

9 - (a^{b} + a^{2} + 3) - (a^{b} + 2)

24 a + 48 b

10 + (- 12)