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Can someone show me how to write complex numbers in standard form? I missed a few days of class and do not have the text book. Answering a simple question like the one below would help

Write the complex number in standard form. $6 + \sqrt{−16}$

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    @JyrkiLahtonen, one of the votes to reopen is explained in one of the answers here: https://math.meta.stackexchange.com/questions/28348/downvote-close-delete2018-05-05

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$\sqrt{-1}$ is written as just $i$ for "imaginary".

$\sqrt{-x}$ can be factored as $\sqrt{-1\vphantom{x}}\sqrt{x} = i\sqrt{x}$.

"Standard form" for complex numbers is $a + bi$ where $a$ and $b$ are real numbers. If $a$ or $b$ is 0, you omit that part. For example, you write $3 + 0i$ as just $3$, and $0 + 3i$ as just $3i$.

For your example, you have $6+\sqrt{-16} = 6 + i\sqrt{16} = 6 + 4i$. The "standard form" is $6+4i$.

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    You have to be carefull, when defining the imaginary unit as you did, see https://en.wikipedia.org/wiki/Imaginary_unit#Proper_use - the correct way is, to say that \(i\) is defined by \(i^2 = -1\), which is note the same as your definition (to be precise, the root is not defined for complex numbers).2013-12-16
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Note that $i^2=-1$, so $\sqrt{-16}=\sqrt{i^216}=i4. $ Hence $6+\sqrt {-16}=6+i4{}$

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    $i\sqrt3$ is fine. $i4$ is bizarre. It looks like someone meant $i_4$ but couldn't find the underscore key.2012-05-29