Home

Roots of Complex Numbers Calculator

Online nth roots: get all n roots with modulus r^(1/n) and arguments (θ+360k)/n.

展开更多 ▾
Roots: r^(1/n)[cos((θ+360k)/n)+i sin]
Modulus
Angle
Positive integer

📖 Tutorial | Roots

1. Definition
There are n nth roots: modulus r^(1/n), arguments (θ+360k)/n, k=0,…,n−1, equally spaced on a circle.
2. Formula & Notation
n,kCount, index
3. Properties & Laws
  • n roots;
  • Equal angular spacing (360/n);
  • Modulus r^(1/n);
  • Real roots a special case.
4. Steps
  1. Enter r,θ,n;
  2. Click "Roots";
  3. Or click "Load Example".
5. Worked Examples
Example: roots of i (r=1,θ=90): ±(0.7071+0.7071i).
6. Common Pitfalls
Do not miss roots;
Add 360k;
Take the nth root of modulus.

❓ FAQ | Roots

How many?
n.
Spacing?
Equal.
Modulus?
r^(1/n).
Real?
Special.
Example?
±(0.7071+0.7071i).
k?
0 to n−1.