Solve a quadratic using square root method

Question

Two problems, question at the end:

#1:

2y^2+4 =0

1)subtract 4 from both sides

2)divide both sides by two

3)square both sides

y= /-2

y= i / 2 or - i /2

#2:

-2w^2-32=0

1)add 32 to both sides

2)divide both sides by -2

w=-16

w=4i or -4i

I am comfortably able to solve these equations and am just wondering why the answers in these problems look different. In problem #1, the answer involves the i coming first. And in #2 the answer has the i coming after the number. Please clarify my confusion.

Answer 1

2y^2+4=0

2y^2=-4

y^2=-2

y=±√(-2)

y=±√[(2)(-1)]

y=±√2*√(-1)

√(-1)=i

y=(±√2)i or y=(√2)i and y=(-√2)i

Answer 2

This is because in the first answer, you are dividing i by 2. In division, it matters which number is on top (numerator) and which number is on bottom (denominator). The second answer is i multipilied by 4. The order of the numbers doesn't matter in multiplication, so it could be written as 4i or i4. However, it is standard in math to put the variable after the constant, which is why the answer is written as 4i. Does this make sense?