This worksheet graphs a number N, using sliders for the angle and modulus, and finds the 2 square roots of N. The roots are are and .

Experiment: Manipulate N (click and drag) and see the relationships involving the 2 square roots.
Uncheck the three boxes showing the values for the numbers.
Questions:Q1. Move N so that the angle is 60 and the modulus is 1. What are the values for the two square roots:

angle,

modulus (distance from the origin).

Q2. Move N so that the angle is 90 and the modulus is 1 (N = 0 + 1i, which is the number i). What are the values for the two square roots:

angle,

modulus (distance from the origin), and

a + bi.

(You found the two square roots of i.)
Q3. Move N so that the angle is 180 and the modulus is 1 (N = -1 + 0i, which is the real number -1). What are the values for the two square roots:

angle,

modulus (distance from the origin), and

a + bi.

(You found the two square roots of -1.)
Q4. Move N so that the angle is -20 and the modulus is 2. What are the values for the two square roots:

angle,

modulus (distance from the origin), and

[You can check your answers by checking the three checkboxes to reveal the values.]