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

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

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

simplify

\frac{3 i}{i + 2}

1 + 2 i

Solution steps

\frac{3 i}{i + 2}

Rewrite

i + 2

in standard complex form:

2 + i

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

Multiply by the conjugate

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

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

Simplify

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

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

Rewrite in standard complex form:

1 + 2 i

= 1 + 2 i

(x - 1) (x + 1) (x + 2) \leq 0

\frac{p}{8} = \frac{7}{9}

(x - 9) (x + 3) = 0

(- 25) (- 36)

- 6 = a (5 - 2)^{2} - 3