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

The solution to (3-i)/(sqrt(2)+3i) is (3sqrt(2)-3)/(11)+(-9-sqrt(2))/(11)i

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

simplify

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

\frac{3 2 - 3}{11} + \frac{- 9 - 2}{11} i

Solution steps

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

Multiply by the conjugate

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

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

Simplify

\frac{( 3 - i ) ( 2 - 3 i )}{( 2 + 3 i ) ( 2 - 3 i )} : \frac{3 2 - 3 + ( - 9 - 2 ) i}{11}

= \frac{3 2 - 3 + ( - 9 - 2 ) i}{11}

Rewrite in standard complex form:

\frac{3 2 - 3}{11} + \frac{- 9 - 2}{11} i

= \frac{3 2 - 3}{11} + \frac{- 9 - 2}{11} i

∣ 4 - 6 ∣

- 4 - - 36

t^{2} - 28 t - 60

\frac{( - 8 )}{4}

1 - \frac{1}{x ^{2}}

What is (3-i)/(sqrt(2)+3i) ?
The solution to (3-i)/(sqrt(2)+3i) is (3sqrt(2)-3)/(11)+(-9-sqrt(2))/(11)i