Giving brainliest Simplify complex numbers

I understand the answers are
2i(square root) 3
and 3i(Square root) 5

I need to understand *how* i comes into the equation and what it does step by step.

You got the answers correct.

Step-by-step explanation:

i is equal to the square root of -1. This is helpful to know because you have to sort of "take out" the negative square root of 1 before simplifying these. the square root of negative 12 is the same thing as the square root of -1 times the square root of 12. Since i is the square root of -1, you can replace that part with i. So, it is i times the square root of 12. We can simplify the square root of 12 by doing the square root of 4 times 3, which is 2 root 3, like you were saying. Then, this value is multiplied by i, so the final answer is 2i (root) 3. This same thing applies to the second portion. The square root of 45 is 3 root 5, and you have to multiply that by i since it is a negative square root. Therefore, that is 3i (root) 5. Comment on my answer if you need a further clarification:)

34.5 cm

step-by-step explanation:

generally for a circular segment of angle, θ° and radius r

arc length

= (θ/360) x circumference

= (θ/360) x 2πr

in our case, θ = 60°, π=3.142 and r = 33 cm

substitute into above formula

arc length

= (60/360) x 2(3.142)( 33) = 34.5 cm