What is 5sqrt(-2)(4+sqrt(-10)) ?

The solution to 5sqrt(-2)(4+sqrt(-10)) is -10sqrt(5)+20sqrt(2)i

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simplify 5sqrt(-2)(4+sqrt(-10))

simplify

5 - 2 (4 + - 10)

- 105 + 202 i

Solution steps

5 - 2 (4 + - 10)

- 2 = 2 i

= 52 i (4 + - 10)

- 10 = 10 i

= 52 i (4 + 10 i)

Apply the distributive law:

a (b + c) = ab + a c

52 i (4 + 10 i) = 52 i 4 + 52 i 10 i

= 52 i 4 + 52 i 10 i

Simplify

52 i 4 + 52 i 10 i : 202 i - 105

= 202 i - 105

Rewrite in standard complex form:

- 105 + 202 i

= - 105 + 202 i

(64 a^{16})^{\frac{1}{4}}

\frac{5 + 4 i}{2 i}

\frac{5}{3} - \frac{7}{6}

(25 z^{4})^{\frac{- 3}{2}}

1 - 125 k^{3}

What is 5sqrt(-2)(4+sqrt(-10)) ?
The solution to 5sqrt(-2)(4+sqrt(-10)) is -10sqrt(5)+20sqrt(2)i