Complex Numbers and Polar Coordinates - Examples & Applications

Interactive Simulators

Interactive Complex Roots Visualizer

Use this tool to explore how taking the

n

-th root of a complex number generates

n

distinct points symmetrically arranged on the complex plane.

Real Part (a): 1.0

Imaginary Part (b): 0.0

Number of Roots (

n

): 3

Original Number ( $z$ ):

z = 1.0 + 0.0i

|z| = r =

1.00

\theta =

0°

Roots ( $w_k$ ):

w_0 = \sqrt[3]{1.0} \left(\cos(0^\circ) + i\sin(0^\circ)\right)

Roots are spaced by 120.0°

Solved Problems

Problem 1: Convert

z = -1 + i\sqrt{3}

to polar form.

0 of 3 Steps Completed

Problem 2: Use De Moivre's Theorem to evaluate

(1 + i)^8

0 of 4 Steps Completed

Problem 3: Find the three cube roots of

8i

0 of 5 Steps Completed

Interactive Simulators