Part (i)

There are 4 roots, so they will be θ = 90° apart.

I First root:

= 3(cos15° + jsin15°) = 2.90 + 0.78j

II Second root:

Add 90° to the first root:

3(cos(15° + 90°) + jsin(15° + 90°))

= 3(cos105° + jsin105°) = -0.78 + 2.90j

So the first 2 fourth roots of 81(cos60° + jsin60°) are:

2.90 + 0.78j and -0.78 + 2.90j

Part (ii)

In each case, r = 81^1/4 = 3