This worksheet graphs a number N 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 N = 2 + 0i (which is the real number 2). 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 2.)
Q2. Move N so that 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 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. (challenge Move N so that N = 2 + 2i. What are the values for the two square roots:

angle (exact),

modulus (estimate) (distance from the origin), and

a + bi (estimate).

(You found the two square roots of 2 + 2i.)
[You can check your answers by checking the three checkboxes to reveal the values.]