Question

1. Find (-1+i)^1/3

2. Express 2(cos5pi/3 + isin5pi/3) in regular form.
would this be correct: 1-√3i?

3. Find (2+4i)^3 in regular form.

4. Express 5(cos5pi/6 + isin5pi/6) in regular form.
would this be correct?: -5√3/2 +5/2i?

Answer 1

I find on powers of complex numbers, it is easier to just go to polar form.

For instance

(-1+i)^(1/3)

put it in polar..
(sqrt2 @135 )^1/3

2^(1/6)@135/3= 1.122@45
= 1.122cos45+i*1.122sin45
= 1.122*.707 + i*1.122*.707

then the other one
(2+4i)=sqrt20@[email protected] so
(2+4i)^3= 20^1.5 @87.14*3=89.4@267
= 89.4(cos267+isin267) and you can simplify that.

Answer 2

#2 and #4 are correct