Precal if you could could you answer both. me finishing this me graduate.

Exercise 1:

The easiest way to compute powers of complex numbers is to write them in the form

In this form, you have

The magnitude of the number is given by

So, we have

As for the angle, we have

So, we have

Finally,

Exercise 2:

You simply have to compute the trigonometric function:

So, we have

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