Complex Root Calculator

Your details

Choose how to display each computed root.
Enter z in Cartesian or polar form.
The real part of the complex number z = a + bi.
The imaginary part of the complex number z = a + bi.
The order of the root: 2 = square root, 3 = cube root, etc. Max 20.
How many decimal places to show in each root.
Modulus of z
1.414214

The absolute value |z| = sqrt(a^2 + b^2)

Argument of z0.785398rad
Root modulus (|z|^(1/n))1.189207
Root count2 distinct roots on a circle of radius 1.1892
Root 1 (k=0)1.0987 + 0.4551i
Root 2 (k=1)-1.0987 - 0.4551i
Angle spacing3.1416 rad (180.0000 deg) = 2*pi / 2
z in polar form1.4142 * (cos(0.7854) + i*sin(0.7854))
z in exponential form1.4142 * e^(i * 0.7854)
|z| (modulus)1.414214
Root modulus1.189207

z = 1.0000 + 1.0000i has 2 distinct square roots.

  • The 2 roots all lie on a circle of radius 1.1892 in the complex plane.
  • Consecutive roots are separated by 180.0000 degrees (3.1416 rad).
  • For a square root the two solutions are always negatives of each other: w1 = -w0.

Next stepVerify any root by raising it to the power n: if the result equals your original z, the computation is correct.

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