What is (isqrt(2)-5)/(i+sqrt(2)) ?

The solution to (isqrt(2)-5)/(i+sqrt(2)) is -(4sqrt(2))/3+7/3 i

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simplify (isqrt(2)-5)/(i+sqrt(2))

simplify

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

- \frac{4 2}{3} + \frac{7}{3} i

Solution steps

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

Rewrite

i 2 - 5

in standard complex form:

- 5 + 2 i

Rewrite

i + 2

in standard complex form:

2 + i

= \frac{- 5 + 2 i}{2 + i}

Multiply by the conjugate

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

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

Simplify

\frac{( - 5 + 2 i ) ( 2 - i )}{( 2 + i ) ( 2 - i )} : \frac{7 i - 4 2}{3}

= \frac{7 i - 4 2}{3}

Rewrite in standard complex form:

- \frac{4 2}{3} + \frac{7}{3} i

= - \frac{4 2}{3} + \frac{7}{3} i

\frac{6 x}{3} + 5 = 1 x + 10

\frac{8 x ^{2} + 3}{5} = 15

- \frac{3}{5} x = 9

8^{2} + 4^{2} = x^{2}

x^{2} + 3 x = 10

What is (isqrt(2)-5)/(i+sqrt(2)) ?
The solution to (isqrt(2)-5)/(i+sqrt(2)) is -(4sqrt(2))/3+7/3 i