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ra1l [238]
3 years ago
8

Which expression is the equivalent to (4+7i)(3+4i)

Mathematics
1 answer:
murzikaleks [220]3 years ago
4 0

Answer:

-16 + 37i

Step-by-step explanation:

First expand.

You get 12 + 16i + 21i + 28i^2.

Because i=\sqrt{-1}, you get 12 + 37i - 28 or -16 + 37i. \blacksquare

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The expression to transform is:

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Let's work first on the inside of the parenthesis.

Recall that the n-root of an expression can be written as a fractional exponent of the expression as follows:

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Therefore \sqrt[6]{a} = a^{\frac{1}{6}}

Now let's replace a with x^{5} which is the algebraic form we are given inside the 6th root:

\sqrt[6]{x^5} = (x^5)^{\frac{1}{6}}

Now use the property that tells us how to proceed when we have  "exponent of an exponent":

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Therefore we get:  (x^5)^{\frac{1}{6}}=x^{\frac{5}{6}}}

Finally remember that this expression was raised to the power 7, therefore:

[tex](\sqrt[6]{x^5})^7=(x^\frac{5}{6})^7=x^\frac{35}{6}[/tex]

An use again the property for the exponent of a exponent:

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