Please simplify these and explain thoroughly what you did. The problems are in the picture attached. I believe them to be complex numbers. Thank you for your help and time.

- i

i

Step-by-step explanation:

1

take out i which is ():

2

(this above, was just a quick explanation on how i^3 is -i)

3

lets use the reference of :

49/4= 12 remainder 1

Using above knowledge

=

(1)12 × i =

1 × i =

i

1\ 8.66i

2\ -i

Step-by-step explanation:

1\

2\

3\

Using the same steps..

step-by-step explanation:

the shape,the size and the distance

we have three similar triangles, because each has a right angle and shares an angle.   let's write the angles in order: opposite to short leg, long leg, hypotenuse.

cab similar to bad similar to cbd

or as ratios,

ca: ab: cb = ba: ad: bd = cb: bd: cd

we also know

ac = ad + cd

(ad+cd): ab: cb = ba: ad: bd = cb: bd: cd

(ad+cd)/cb=cb/cd

we have cb=6, ad=5 and seek x=cd.

we reject the negative root and conclude x=4

answer: 4