When working with a complex number is $\sqrt3i$ the same thing as $i\sqrt3$?
I am currently practicing writing complex numbers in standard form.
The question I was given is: Does $5+\sqrt1i$ = $5+i\sqrt1$? I think it is yes.
Format of Complex Numbers
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$\begingroup$
complex-numbers
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0Multiplication is commutative in a field – 2017-01-29
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0Is the edit ok,or did you mean to put $\sqrt{(3)}$? – 2017-01-29
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0@NUG: The two products are the same, but $\sqrt{3}i$ carries some risk of being mis-read as $\sqrt{3i}$, while $i\sqrt{3}$ doesn't. – 2017-01-29
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0Mathematically, the expressions have the same value, because, as mentioned earlier, multiplication is commutative in a field. Typographically, I think the $i$-first convention is easier to read and clearer to understand. – 2017-01-29
2 Answers
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Multiplication is commutative even within the complex set.
Hence
$$\sqrt{3}i = i\sqrt{3}$$
Hence yes, it's the same.
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Yes, it does. Multiplication is commutative, meaning that $a \cdot b=b\cdot a$ for all $a,b \in \mathbb{C}$.
Therefore, we can apply this to your situation, and let $a=\sqrt{3}$ and $b=i$.
Similarly, you can do the same with the second example and let $a=\sqrt{1}$ and $b=i$.