# Does it matter where we put i?

1. Aug 2, 2015

### JR Sauerland

In this problem, they solve for i, and at first, it looks like it will be i*2* square root of 3... Then he puts 2 sqrt of 3 times i. Can it also be 2i sqrt of 3?

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2. Aug 2, 2015

### Borg

It doesn't matter where you put it as long as it's clear whether i is inside the square root or not. Also, it looks like 13 and not 3.

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3. Aug 2, 2015

### JR Sauerland

Oops. I'm still a little sleepy. I'm saying that because someone told me I was wrong. I was seriously confused because I've seen professors write it as 2i sqrt of 13....

4. Aug 2, 2015

### jasonRF

JR Souerland,
The order does not matter. Complex number satisfy the commutative property $z_1 z_2 = z_2 z_1$, for any two complex numbers $z_1$ and $z_2$. They also have the associative property $z_1 (z_2 z_3) = (z_1 z_2) z_3$.

jason

5. Aug 2, 2015

### Staff: Mentor

Yes. But it's better to position the imaginary number i where it will not be easily overlooked, so in an expression write it first or else last, but don't hide it somewhere in the middle.

6. Aug 2, 2015

### Borg

Well from your image, it looks like it says 2i divided by sqrt 13. That would be wrong.

7. Aug 2, 2015

### Staff: Mentor

In that image, you show an expression that includes a division sign. That's presumably why you were told it would not be equivalent?

8. Aug 2, 2015

### JR Sauerland

Yeah, I realized that after. I had gotten used to square root being expressed as /sqrt due to Mathway -_- and mylabsplus also uses /sqrt to create a square root sign lol. Woe is me.