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nataly862011 [7]

2 years ago

10

Complex numbers simplify square roots of negative numbers

2 answers:

sergey [27]2 years ago

8 0

Step-by-step explanation:

√-100

√-(10)²

√10²√-1

10i

0+10i

Bogdan [553]2 years ago

3 0

Lets do

$\\ \sf\longmapsto \sqrt{-100}$

$\\ \sf\longmapsto \sqrt{-(10)^2}$

$\\ \sf\longmapsto \sqrt{10^2}\sqrt{-1}$

$\\ \sf\longmapsto 10i$

Write in standard form

$\\ \sf\longmapsto 10i$

$\\ \sf\longmapsto \boxed{0}+\boxed{10}i$

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Use long division to divide x^3+x^2-2x+14 by x+3

bekas [8.4K]

First, $x^3=x^2\cdot x$ , and if we multiply $x+3$ by $x^2$ we get

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Subtracting this from the numerator gives a remainder of

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Next, $-2x^2=-2x\cdot x$ , and if we multiply $x+3$ by $-2x$ we have

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and subtracting this from the previous remainder, we end up with a new remainder of

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Next, $4x=4\cdot x$ , and if we multiply $x+3$ by $4$ we get

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Subtracting from the previous remainder, we get a new remainder of

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which contains no more factors of $x$ , so we're done.

So,

$\dfrac{x^3+x^2-2x+14}{x+3}=x^2-2x+4+\dfrac2{x+3}$

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