Square Roots of a Complex Number - With Sliders

Author:: James R Olsen

Topic:: Angles, Function Graph, Root, Square

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.]

Square Roots of a Complex Number - With Sliders

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