What is (4i)/(sqrt(2)+3i) ?

The solution to (4i)/(sqrt(2)+3i) is 12/11+(4sqrt(2))/(11)i

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simplify (4i)/(sqrt(2)+3i)

simplify

\frac{4 i}{2 + 3 i}

\frac{12}{11} + \frac{4 2}{11} i

Solution steps

\frac{4 i}{2 + 3 i}

Multiply by the conjugate

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

= \frac{4 i ( 2 - 3 i )}{( 2 + 3 i ) ( 2 - 3 i )}

Simplify

\frac{4 i ( 2 - 3 i )}{( 2 + 3 i ) ( 2 - 3 i )} : \frac{4 2 i + 12}{11}

= \frac{4 2 i + 12}{11}

Rewrite in standard complex form:

\frac{12}{11} + \frac{4 2}{11} i

= \frac{12}{11} + \frac{4 2}{11} i

4 7^{2}

\frac{x ^{2} + 8 x + 15}{x ^{2} + 6 x + 5}

\frac{56}{6}

(9 - 81) (2)

\frac{3}{5} \div 2 \frac{1}{2}

What is (4i)/(sqrt(2)+3i) ?
The solution to (4i)/(sqrt(2)+3i) is 12/11+(4sqrt(2))/(11)i