# Square Roots of a Complex Number

- Author:
- James R Olsen

- Topic:
- Angles, Function Graph, Root, Square

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.

**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.

**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.

**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).

*check your answers*by checking the three checkboxes to reveal the values.]