Part (i)

There are 4 roots, so they will be `θ = 90^@` apart.

I First root:

`81^(1"/"4)[cos\ ( 60^text(o))/4+j\ sin\ (60^text(o))/4]`

`= 3(cos\ 15^"o" + j\ sin\ 15^"o")`

` = 2.90 + 0.78j`

II Second root:

Add `90°` to the first root:

3(cos(15° + 90°) + j sin(15° + 90°))

= 3(cos105° + j sin 105°)

= -0.78 + 2.90j

So the first 2 fourth roots of 81(cos 60° + j sin 60°) are:

`2.90 + 0.78j` and `-0.78 + 2.90j`

Part (ii)

In each case, r = 811/4 = 3

Fourth complex roots of an equation