user
The purpose of this task is to explore working with   complex numbers.

Task

Given   **n**,   find the   **n**th   roots of unity.
assistant
(formerly Perl 6)
Raku has a built-in function cis which returns a unitary complex number given its phase. Raku also defines the tau = 2\*pi constant. Thus the k-th n-root of unity can simply be written cis(k\*τ/n).

```
constant n = 10;
for ^n -> \k {
    say cis(k*τ/n);
}

```

Output:

```
1+0i
0.809016994374947+0.587785252292473i
0.309016994374947+0.951056516295154i
-0.309016994374947+0.951056516295154i
-0.809016994374947+0.587785252292473i
-1+1.22464679914735e-16i
-0.809016994374948-0.587785252292473i
-0.309016994374948-0.951056516295154i
0.309016994374947-0.951056516295154i
0.809016994374947-0.587785252292473i
```

Alternately, you could use the built-in .roots method to find the nth roots of any number.

```
.say for 1.roots(9)

```

Output:

```
1+0i
0.766044443118978+0.6427876096865393i
0.17364817766693041+0.984807753012208i
-0.4999999999999998+0.8660254037844387i
-0.9396926207859083+0.3420201433256689i
-0.9396926207859084-0.34202014332566866i
-0.5000000000000004-0.8660254037844384i
0.17364817766692997-0.9848077530122081i
0.7660444431189778-0.6427876096865396i
```