Question

Difficult pre calculus stuff.

Answer 1

When we divide complex numbers we divide their magnitudes and subtract their angles, so this isn't all that difficult:

`(10(\cos 45^\circ + i \sin 45^\circ))/(5 (\cos 15^\circ + i \sin 15^\circ)) = (10)/(5) (\cos(45^\circ - 15^\circ) + i \sin(45^\circ - 15^\circ))`

`= 2(\cos 30^\circ + i \sin 30^\circ)`

Answer:
`2(\cos 30^\circ + i \sin 30^\circ)`

That's probably what's called simplified polar form until you get to Euler's Formula. Since it's 30 degrees we can get a nice rectangular form:

`2(\cos 30^\circ + i \sin 30^\circ) = 2\left( (√(3))/(2) + i \frac 1 2 \right) = √(3) + i`